Unsolved Problems In Number Theory

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  unsolved problems in number theory: Unsolved Problems in Number Theory Richard Guy, R.K. Guy, 2013-06-29 To many laymen, mathematicians appear to be problem solvers, people who do hard sums. Even inside the profession we dassify ourselves as either theorists or problem solvers. Mathematics is kept alive, much more than by the activities of either dass, by the appearance of a succession of unsolved problems, both from within mathematics-itself and from the in creasing number of disciplines where it is applied. Mathematics often owes more to those who ask questions than to those who answer them. The solu tion of a problem may stifte interest in the area around it. But Fermat's Last Theorem, because it is not yet a theorem, has generated a great deal of good mathematics, whether goodness is judged by beauty, by depth or byapplicability. To pose good unsolved problems is a difficult art. The balance between triviality and hopeless unsolvability is delicate. There are many simply stated problems which experts tell us are unlikely to be solved in the next generation. But we have seen the Four Color Conjecture settled, even ifwe don't live long enough to leam the status of the Riemann and Goldbach hypotheses, of twin primes or Mersenne primes, or of odd perfeet numbers. On the other hand, unsolved problems may not be unsolved at all, or may be much more tractable than was at first thought.
  unsolved problems in number theory: Unsolved Problems in Number Theory Richard Guy, 2013-11-11 To many laymen, mathematicians appear to be problem solvers, people who do hard sums. Even inside the profession we dassify ouselves as either theorists or problem solvers. Mathematics is kept alive, much more than by the activities of either dass, by the appearance of a succession of unsolved problems, both from within mathematics itself and from the increasing number of disciplines where it is applied. Mathematics often owes more to those who ask questions than to those who answer them. The solution of a problem may stifte interest in the area around it. But Fermat 's Last Theorem, because it is not yet a theorem, has generated a great deal of good mathematics, whether goodness is judged by beauty, by depth or by applicability. To pose good unsolved problems is a difficult art. The balance between triviality and hopeless unsolvability is delicate. There are many simply stated problems which experts tell us are unlikely to be solved in the next generation. But we have seen the Four Color Conjecture settled, even if we don't live long enough to learn the status of the Riemann and Goldbach hypotheses, of twin primes or Mersenne primes, or of odd perfect numbers. On the other hand, unsolved problems may not be unsolved at all, or than was at first thought.
  unsolved problems in number theory: Old and New Unsolved Problems in Plane Geometry and Number Theory Victor Klee, Stan Wagon, 1991-12-31
  unsolved problems in number theory: Solved and Unsolved Problems in Number Theory Daniel Shanks, 2024-01-24 The investigation of three problems, perfect numbers, periodic decimals, and Pythagorean numbers, has given rise to much of elementary number theory. In this book, Daniel Shanks, past editor of Mathematics of Computation, shows how each result leads to further results and conjectures. The outcome is a most exciting and unusual treatment. This edition contains a new chapter presenting research done between 1962 and 1978, emphasizing results that were achieved with the help of computers.
  unsolved problems in number theory: Unsolved Problems in Geometry Hallard T. Croft, Kenneth Falconer, Richard K. Guy, 2012-12-06 Mathematicians and non-mathematicians alike have long been fascinated by geometrical problems, particularly those that are intuitive in the sense of being easy to state, perhaps with the aid of a simple diagram. Each section in the book describes a problem or a group of related problems. Usually the problems are capable of generalization of variation in many directions. The book can be appreciated at many levels and is intended for everyone from amateurs to research mathematicians.
  unsolved problems in number theory: Unsolved Problems on Mathematics for the 21st Century Kiyoshi Iseki, 2001
  unsolved problems in number theory: Erdös on Graphs Fan Chung, Ron Graham, At&T Labs, 2020-08-26 This book is a tribute to Paul Erdos, the wandering mathematician once described as the prince of problem solvers and the absolute monarch of problem posers. It examines the legacy of open problems he left to the world after his death in 1996.
  unsolved problems in number theory: Unsolved Problems in Number Theory Richard Guy, 2004-07-13 Mathematics is kept alive by the appearance of new, unsolved problems. This book provides a steady supply of easily understood, if not easily solved, problems that can be considered in varying depths by mathematicians at all levels of mathematical maturity. This new edition features lists of references to OEIS, Neal Sloane’s Online Encyclopedia of Integer Sequences, at the end of several of the sections.
  unsolved problems in number theory: Unsolved Problems in Number Theory Richard Guy, 2014-01-15
  unsolved problems in number theory: Number Theory and Its History Oystein Ore, 2012-07-06 Unusually clear, accessible introduction covers counting, properties of numbers, prime numbers, Aliquot parts, Diophantine problems, congruences, much more. Bibliography.
  unsolved problems in number theory: Solved and Unsolved Problems in Number Theory Daniel Shanks, 1901
  unsolved problems in number theory: Unsolved Problems in Number Theory Richard K. Guy, 1994
  unsolved problems in number theory: Mage Merlin's Unsolved Mathematical Mysteries Satyan Devadoss, Matthew Harvey, 2020-07-28 Sixteen of today's greatest unsolved mathematical puzzles in a story-driven, illustrated volume that invites readers to peek over the edge of the unknown. Most people think of mathematics as a set of useful tools designed to answer analytical questions, beginning with simple arithmetic and ending with advanced calculus. But, as Mage Merlin's Unsolved Mathematical Mysteries shows, mathematics is filled with intriguing mysteries that take us to the edge of the unknown. This richly illustrated, story-driven volume presents sixteen of today's greatest unsolved mathematical puzzles, all understandable by anyone with elementary math skills. These intriguing mysteries are presented to readers as puzzles that have time-traveled from Camelot, preserved in the notebook of Merlin, the wise magician in King Arthur's court. Our guide is Mage Maryam (named in honor of the brilliant young mathematician, the late Maryam Mirzakhani), a distant descendant of Merlin. Maryam introduces the mysteries—each of which is presented across two beautifully illustrated pages—and provides mathematical and historical context afterward. We find Merlin confronting mathematical puzzles involving tinker toys (a present for Camelot's princesses from the sorceress Morgana), cake-slicing at a festival, Lancelot's labyrinth, a vault for the Holy Grail, and more. Each mystery is a sword awaiting removal from its stone, capturing the beauty and power of mathematics.
  unsolved problems in number theory: Problems in Algebraic Number Theory M. Ram Murty, Jody Esmonde, 2005 The problems are systematically arranged to reveal the evolution of concepts and ideas of the subject Includes various levels of problems - some are easy and straightforward, while others are more challenging All problems are elegantly solved
  unsolved problems in number theory: Gamma Julian Havil, 2017-10-31 Among the myriad of constants that appear in mathematics, p, e, and i are the most familiar. Following closely behind is g, or gamma, a constant that arises in many mathematical areas yet maintains a profound sense of mystery. In a tantalizing blend of history and mathematics, Julian Havil takes the reader on a journey through logarithms and the harmonic series, the two defining elements of gamma, toward the first account of gamma's place in mathematics. Introduced by the Swiss mathematician Leonhard Euler (1707-1783), who figures prominently in this.
  unsolved problems in number theory: Abstract analytic number theory Knopfmacher, 2009-02-04 North-Holland Mathematical Library, Volume 12: Abstract Analytic Number Theory focuses on the approaches, methodologies, and principles of the abstract analytic number theory. The publication first deals with arithmetical semigroups, arithmetical functions, and enumeration problems. Discussions focus on special functions and additive arithmetical semigroups, enumeration and zeta functions in special cases, infinite sums and products, double series and products, integral domains and arithmetical semigroups, and categories satisfying theorems of the Krull-Schmidt type. The text then ponders on semigroups satisfying Axiom A, asymptotic enumeration and statistical properties of arithmetical functions, and abstract prime number theorem. Topics include asymptotic properties of prime-divisor functions, maximum and minimum orders of magnitude of certain functions, asymptotic enumeration in certain categories, distribution functions of prime-independent functions, and approximate average values of special arithmetical functions. The manuscript takes a look at arithmetical formations, additive arithmetical semigroups, and Fourier analysis of arithmetical functions, including Fourier theory of almost even functions, additive abstract prime number theorem, asymptotic average values and densities, and average values of arithmetical functions over a class. The book is a vital reference for researchers interested in the abstract analytic number theory.
  unsolved problems in number theory: 250 Problems in Elementary Number Theory Wacław Sierpiński, 1970
  unsolved problems in number theory: Unsolved Problems in Number Theory R. K. Guy, 2014-01-15
  unsolved problems in number theory: Gösta Mittag-Leffler Arild Stubhaug, 2010-08-03 Gösta Mittag-Leffler (1846–1927) played a significant role as both a scientist and entrepreneur. Regarded as the father of Swedish mathematics, his influence extended far beyond his chosen field because of his extensive network of international contacts in science, business, and the arts. He was instrumental in seeing to it that Marie Curie was awarded the Nobel Prize twice. One of Mittag-Leffler’s major accomplishments was the founding of the journal Acta Mathematica , published by Institut Mittag-Leffler and Sweden’s Royal Academy of Sciences. Arild Stubhaug’s research for this monumental biography relied on a wealth of primary and secondary resources, including more than 30000 letters that are part of the Mittag-Leffler archives. Written in a lucid and compelling manner, the biography contains many hitherto unknown facts about Mittag-Leffler’s personal life and professional endeavors. It will be of great interest to both mathematicians and general readers interested in science and culture.
  unsolved problems in number theory: Prime Numbers and the Riemann Hypothesis Barry Mazur, William Stein, 2016-04-11 This book introduces prime numbers and explains the famous unsolved Riemann hypothesis.
  unsolved problems in number theory: Advanced Problems in Mathematics: Preparing for University Stephen Siklos, 2016-01-25 This book is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge colleges as the basis for conditional offers. They are also used by Warwick University, and many other mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination. Advanced Problems in Mathematics is recommended as preparation for any undergraduate mathematics course, even for students who do not plan to take the Sixth Term Examination Paper. The questions analysed in this book are all based on recent STEP questions selected to address the syllabus for Papers I and II, which is the A-level core (i.e. C1 to C4) with a few additions. Each question is followed by a comment and a full solution. The comments direct the reader's attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently. This book is a must read for any student wishing to apply to scientific subjects at university level and for anybody interested in advanced mathematics.
  unsolved problems in number theory: Elliptic Tales Avner Ash, Robert Gross, 2012 Describes the latest developments in number theory by looking at the Birch and Swinnerton-Dyer Conjecture.
  unsolved problems in number theory: Problem-Solving and Selected Topics in Number Theory Michael Th. Rassias, 2010-11-16 The book provides a self-contained introduction to classical Number Theory. All the proofs of the individual theorems and the solutions of the exercises are being presented step by step. Some historical remarks are also presented. The book will be directed to advanced undergraduate, beginning graduate students as well as to students who prepare for mathematical competitions (ex. Mathematical Olympiads and Putnam Mathematical competition).
  unsolved problems in number theory: Unsolved Problems in Number Theory Richard Guy, 2014-01-15
  unsolved problems in number theory: The Millennium Problems Keith J. Devlin, 2005 In 2000, the Clay Foundation of Cambridge, Massachusetts, announced a historic competition: Whoever could solve any of seven extraordinarily difficult mathematical problems, and have the solution acknowledged as correct by the experts, would receive $1million in prize money. They encompass many of the most fascinating areas of pure and applied mathematics, from topology and number theory to particle physics, cryptography, computing and even aircraft design. Keith Devlin describes here what the seven problems are, how they came about, and what they mean for mathematics and science. In the hands of Devlin, each Millennium Problem becomes a fascinating window onto the deepest questions in the field.
  unsolved problems in number theory: Love and Math Edward Frenkel, 2014-09-09 An awesome, globe-spanning, and New York Times bestselling journey through the beauty and power of mathematics What if you had to take an art class in which you were only taught how to paint a fence? What if you were never shown the paintings of van Gogh and Picasso, weren't even told they existed? Alas, this is how math is taught, and so for most of us it becomes the intellectual equivalent of watching paint dry. In Love and Math, renowned mathematician Edward Frenkel reveals a side of math we've never seen, suffused with all the beauty and elegance of a work of art. In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space. Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man's journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century's leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat's last theorem, that had seemed intractable before. At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics.
  unsolved problems in number theory: Unsolved Problems in Intuitive Mathematics Richard K. Guy, 1994
  unsolved problems in number theory: Model-Theoretic Logics J. Barwise, Solomon Feferman, S. Feferman, 2017-03-02 This book brings together several directions of work in model theory between the late 1950s and early 1980s.
  unsolved problems in number theory: Prime Numbers David Wells, 2011-01-13 A fascinating journey into the mind-bending world of prime numbers Cicadas of the genus Magicicada appear once every 7, 13, or 17 years. Is it just a coincidence that these are all prime numbers? How do twin primes differ from cousin primes, and what on earth (or in the mind of a mathematician) could be sexy about prime numbers? What did Albert Wilansky find so fascinating about his brother-in-law's phone number? Mathematicians have been asking questions about prime numbers for more than twenty-five centuries, and every answer seems to generate a new rash of questions. In Prime Numbers: The Most Mysterious Figures in Math, you'll meet the world's most gifted mathematicians, from Pythagoras and Euclid to Fermat, Gauss, and Erd?o?s, and you'll discover a host of unique insights and inventive conjectures that have both enlarged our understanding and deepened the mystique of prime numbers. This comprehensive, A-to-Z guide covers everything you ever wanted to know--and much more that you never suspected--about prime numbers, including: * The unproven Riemann hypothesis and the power of the zeta function * The Primes is in P algorithm * The sieve of Eratosthenes of Cyrene * Fermat and Fibonacci numbers * The Great Internet Mersenne Prime Search * And much, much more
  unsolved problems in number theory: The Theory of Numbers Andrew Adler, John E. Coury, 1995
  unsolved problems in number theory: Intuitive Geometry Imre Bárány, K. Böröczky, 1997
  unsolved problems in number theory: A Course in Number Theory H. E. Rose, 1995 The second edition of this undergraduate textbook is now available in paperback. Covering up-to-date as well as established material, it is the only textbook which deals with all the main areas of number theory, taught in the third year of a mathematics course. Each chapter ends with a collection of problems, and hints and sketch solutions are provided at the end of the book, together with useful tables.
  unsolved problems in number theory: Exploring Mathematics Daniel Grieser, 2018-05-31 Have you ever faced a mathematical problem and had no idea how to approach it? Or perhaps you had an idea but got stuck halfway through? This book guides you in developing your creativity, as it takes you on a voyage of discovery into mathematics. Readers will not only learn strategies for solving problems and logical reasoning, but they will also learn about the importance of proofs and various proof techniques. Other topics covered include recursion, mathematical induction, graphs, counting, elementary number theory, and the pigeonhole, extremal and invariance principles. Designed to help students make the transition from secondary school to university level, this book provides readers with a refreshing look at mathematics and deep insights into universal principles that are valuable far beyond the scope of this book. Aimed especially at undergraduate and secondary school students as well as teachers, this book will appeal to anyone interested in mathematics. Only basic secondary school mathematics is required, including an understanding of numbers and elementary geometry, but no calculus. Including numerous exercises, with hints provided, this textbook is suitable for self-study and use alongside lecture courses.
  unsolved problems in number theory: The Ultimate Challenge Jeffrey C. Lagarias, 2023-04-19 The $3x+1$ problem, or Collatz problem, concerns the following seemingly innocent arithmetic procedure applied to integers: If an integer $x$ is odd then “multiply by three and add one”, while if it is even then “divide by two”. The $3x+1$ problem asks whether, starting from any positive integer, repeating this procedure over and over will eventually reach the number 1. Despite its simple appearance, this problem is unsolved. Generalizations of the problem are known to be undecidable, and the problem itself is believed to be extraordinarily difficult. This book reports on what is known on this problem. It consists of a collection of papers, which can be read independently of each other. The book begins with two introductory papers, one giving an overview and current status, and the second giving history and basic results on the problem. These are followed by three survey papers on the problem, relating it to number theory and dynamical systems, to Markov chains and ergodic theory, and to logic and the theory of computation. The next paper presents results on probabilistic models for behavior of the iteration. This is followed by a paper giving the latest computational results on the problem, which verify its truth for $x < 5.4 cdot 10^{18}$. The book also reprints six early papers on the problem and related questions, by L. Collatz, J. H. Conway, H. S. M. Coxeter, C. J. Everett, and R. K. Guy, each with editorial commentary. The book concludes with an annotated bibliography of work on the problem up to the year 2000.
  unsolved problems in number theory: In Pursuit of Zeta-3 Paul J. Nahin, 2023-05-16 For centuries, mathematicians have tried, and failed, to solve the zeta-3 problem. This problem is simple in its formulation, but remains unsolved to this day, despite the attempts of some of the world's greatest mathematicians to solve it. The problem can be stated as follows: is there a simple symbolic formula for the following sum: 1+(1/2)^3+(1/3)^3+(1/4)^3+...? Although it is possible to calculate the approximate numerical value of the sum (for those interested, it's 1.20205...), there is no known symbolic expression. A symbolic formula would not only provide an exact value for the sum, but would allow for greater insight into its characteristics and properties. The answers to these questions are not of purely academic interest; the zeta-3 problem has close connections to physics, engineering, and other areas of mathematics. Zeta-3 arises in quantum electrodynamics and in number theory, for instance, and it is closely connected to the Riemann hypothesis. In In Pursuit of zeta-3, Paul Nahin turns his sharp, witty eye on the zeta-3 problem. He describes the problem's history, and provides numerous challenge questions to engage readers, along with Matlab code. Unlike other, similarly challenging problems, anyone with a basic mathematical background can understand the problem-making it an ideal choice for a pop math book--
  unsolved problems in number theory: Discrete Mathematics and Its Applications Kenneth Rosen, 2006-07-26 Discrete Mathematics and its Applications, Sixth Edition, is intended for one- or two-term introductory discrete mathematics courses taken by students from a wide variety of majors, including computer science, mathematics, and engineering. This renowned best-selling text, which has been used at over 500 institutions around the world, gives a focused introduction to the primary themes in a discrete mathematics course and demonstrates the relevance and practicality of discrete mathematics to a wide a wide variety of real-world applications...from computer science to data networking, to psychology, to chemistry, to engineering, to linguistics, to biology, to business, and to many other important fields.
  unsolved problems in number theory: Elementary Number Theory: Primes, Congruences, and Secrets William Stein, 2008-10-28 This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. It grew out of undergr- uate courses that the author taught at Harvard, UC San Diego, and the University of Washington. The systematic study of number theory was initiated around 300B. C. when Euclid proved that there are in?nitely many prime numbers, and also cleverly deduced the fundamental theorem of arithmetic, which asserts that every positive integer factors uniquely as a product of primes. Over a thousand years later (around 972A. D. ) Arab mathematicians formulated the congruent number problem that asks for a way to decide whether or not a given positive integer n is the area of a right triangle, all three of whose sides are rational numbers. Then another thousand years later (in 1976), Di?e and Hellman introduced the ?rst ever public-key cryptosystem, which enabled two people to communicate secretely over a public communications channel with no predeterminedsecret; this invention and the ones that followed it revolutionized the world of digital communication. In the 1980s and 1990s, elliptic curves revolutionized number theory, providing striking new insights into the congruent number problem, primality testing, publ- key cryptography, attacks on public-key systems, and playing a central role in Andrew Wiles’ resolution of Fermat’s Last Theorem.
  unsolved problems in number theory: Problems in Real Analysis Teodora-Liliana Radulescu, Vicentiu D. Radulescu, Titu Andreescu, 2009-06-12 Problems in Real Analysis: Advanced Calculus on the Real Axis features a comprehensive collection of challenging problems in mathematical analysis that aim to promote creative, non-standard techniques for solving problems. This self-contained text offers a host of new mathematical tools and strategies which develop a connection between analysis and other mathematical disciplines, such as physics and engineering. A broad view of mathematics is presented throughout; the text is excellent for the classroom or self-study. It is intended for undergraduate and graduate students in mathematics, as well as for researchers engaged in the interplay between applied analysis, mathematical physics, and numerical analysis.
  unsolved problems in number theory: Old and New Unsolved Problems in Plane Geometry and Number Theory Victor Klee, Stan Wagon, 2020-07-31 Victor Klee and Stan Wagon discuss some of the unsolved problems in number theory and geometry, many of which can be understood by readers with a very modest mathematical background. The presentation is organized around 24 central problems, many of which are accompanied by other, related problems. The authors place each problem in its historical and mathematical context, and the discussion is at the level of undergraduate mathematics. Each problem section is presented in two parts. The first gives an elementary overview discussing the history and both the solved and unsolved variants of the problem. The second part contains more details, including a few proofs of related results, a wider and deeper survey of what is known about the problem and its relatives, and a large collection of references. Both parts contain exercises, with solutions. The book is aimed at both teachers and students of mathematics who want to know more about famous unsolved problems.
Unsolved Mysteries - The Original, Iconic Television Series
Perhaps YOU can help solve a mystery. The original Unsolved Mysteries episodes you know and love are now streaming! See the mysteries and the updates.

About - Unsolved Mysteries
Unsolved Mysteries was first broadcast in January of 1987, and is one of the longest running programs in the history of television. Each episode features four to five segments profiling real …

All New Mysteries - Unsolved Mysteries
It’s official! Unsolved Mysteries is set to return with all new episodes. Deadline article. Press Release

Can you help solve a mystery? - Unsolved Mysteries
Oct 19, 2020 · Watch Volume 1 of Unsolved Mysteries now on Netflix. Six all new episodes coming October 19th! See the official trailer for Volume 2: “

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Case categories include: Murder, Missing Persons, Wanted Fugitives, UFOs, Ghosts, Amnesia, Fraud, and more. Help solve a mystery!

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Bottom line/ had unsolved mysteries not done the show they did on the case, Patry would still be in prison, still be innocent and mr. McElroy would be to blame. She was freed DESPITE his attempt …

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The bodies of Mike and Cathy Scott, and their two elderly mothers, are sprawled across the blood-soaked floor of their Pendleton, SC home. Seven years later, the brutal quadruple homicide …

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Curious if Mysterious Mutilations Case Were Solved? Find Out Answer on Unsolved Mysteries Broadcast Website. Unsolved Mysteries Also Includes Cases Related to Murder, Missing Persons, …

Unsolved Mysteries - The Original, Iconic Television Series
Perhaps YOU can help solve a mystery. The original Unsolved Mysteries episodes you know and love are now streaming! See the mysteries and the updates.

About - Unsolved Mysteries
Unsolved Mysteries was first broadcast in January of 1987, and is one of the longest running programs in the history of television. Each episode features four to five segments profiling real …

All New Mysteries - Unsolved Mysteries
It’s official! Unsolved Mysteries is set to return with all new episodes. Deadline article. Press Release

Can you help solve a mystery? - Unsolved Mysteries
Oct 19, 2020 · Watch Volume 1 of Unsolved Mysteries now on Netflix. Six all new episodes coming October 19th! See the official trailer for Volume 2: “

Where to Watch - Unsolved Mysteries
Need an Unsolved Mysteries fix? You can now stream the Robert Stack & Dennis Farina episodes on:

Join us in celebrating the 35th anniversary of Unsolved Mysteries!
Unsolved Mysteries: Behind The Legacy is now available to stream on multiple platforms! Check out your favorite FilmRise partners to see where you can watch. #UnsolvedMysteries35

Archived Cases - Unsolved Mysteries
Case categories include: Murder, Missing Persons, Wanted Fugitives, UFOs, Ghosts, Amnesia, Fraud, and more. Help solve a mystery!

Patty Stallings - Unsolved Mysteries
Bottom line/ had unsolved mysteries not done the show they did on the case, Patry would still be in prison, still be innocent and mr. McElroy would be to blame. She was freed DESPITE his …

Podcast - Unsolved Mysteries
The bodies of Mike and Cathy Scott, and their two elderly mothers, are sprawled across the blood-soaked floor of their Pendleton, SC home. Seven years later, the brutal quadruple …

Discover Mysterious Mutilations Case - Unsolved Mysteries
Curious if Mysterious Mutilations Case Were Solved? Find Out Answer on Unsolved Mysteries Broadcast Website. Unsolved Mysteries Also Includes Cases Related to Murder, Missing …