UNSOLVED PROBLEMS |

In Number Theory, Logic, and Cryptography |

Archive of Contributions and Proposed Solutions |

This page contains links to some contributions published more than one year ago.
#85: A contribution to the Goldbach Conjecture. Submitted by Graham Cooper, 11.30 GMT, Friday 29th April 2016. Click here for full text.
#83: A contribution to the Perfect Cuboid Problem. Submitted by Lee Morgenstern, 21.00 GMT, Thursday 24th March 2016. “A new approach is given …. proving many special cases impossible using inequality relationships…” Click here for full text.
#82: A contribution to the Collatz Conjecture. Submitted by Solomon Beyene, 14.00 GMT, Saturday 19th March 2016. Click here for full text.
#81: A contribution to the K-tuple Conjecture. Submitted by Kim Lumbard, 22.30 GMT, Monday 15th February 2016. “The k-tuple Conjecture is true. The pure elimination sieve finds all prime instances of a k-tuple H…” Click here for full text.
#80: A contribution to Fermat’s Last Theorem. Submitted by J Yun 15.30 GMT, Thursday 31st December 2015. “This paper offers a concise proof of Fermat’s Last Theorem using the Euclidean algorithm.” Click here for full text.
#74: A contribution to the Collatz Conjecture. Submitted by Antoine Mhanna, 01.45 GMT, Friday 23rd October 2015, revised version submitted 11.00 GMT, Monday 9th November 2015. Click here for full text.
#73: A contribution to Brocard’s Problem. Submitted by Robert D Matson, 17.30 GMT, Thursday 17th September 2015. “The purpose of this paper is to report on recent calculations that extend the lower limit on any fourth solution to the Brocard Problem by more than two orders of magnitude to n > 400 billion.“ Click here for full text.
#70: A contribution to the Perfect Cuboid Problem. Submitted by Terry Raines, 14.15 GMT, Wednesday 5th August 2015. “I discovered the following simple method which seems to generalize most of the older search methods….it will find every primitive body cuboid exactly once.” Click here for full text.
#69: A contribution to Elgar’s Music Box Cipher. Submitted by Robert Padgett, 15.30 GMT, Monday 3rd August 2015. “Elgar loved puns, acrostics, secret codes and crossword puzzles. It should come as no surprise the Enigma Variations harbor numerous ciphers that encode the solutions to its three central riddles:” Click here for full text.
#68: A contribution to the Riemann Hypothesis. Submitted by Choe Ryong Gil , 04.35 GMT, Thursday 23rd July 2015. “In this paper we consider the Riemann hypothesis by the primorial numbers.” Click here for full text.
#66: A contribution to the Magic Square of Squares Problem. Submitted by Tim Thaler, 21.30 GMT, Tuesday 31st March 2015. “This article will prove that a 3 by 3 magic square with all entries as unique integer perfect squares does not exist.”. Click here for full text.
#65: A contribution to Brocard’s Problem. Submitted by Scott Hamilton, 00.45 GMT, Wednesday 26th March 2015. “This paper will conclusively demonstrate that no more than three solutions exist” . Click here for full text.
#64: A contribution to the Perfect Cuboid Problem. Submitted by Terry Raines, 17.30 GMT, Friday 20th March 2015. “Cuboid Parametric Formulas” . Click here for full text.
#63: A contribution to the Legendre Conjecture. Submitted by Edigles Guedes , 12.15 GMT, Friday 20th March 2015. “Three Proofs for Legendre’s Conjecture” . Click here for full text.
#62: A contribution to the Perfect Cuboid Problem. Submitted by Mamuka Meskhishvili , 11.30 GMT, Wednesday 11th February 2015. “Parametric Solutions for a Nearly-Perfect Cuboid” . Click here for full text.
#61: A contribution to the Perfect Cuboid Problem. Submitted by Mamuka Meskhishvili , 11.30 GMT, Wednesday 11th February 2015. “Perfect Cuboid and Congruent Number Equation Solutions” . Click here for full text.
#60: A contribution to the Perfect Cuboid Problem. Submitted by Terry Raines, 9.30 GMT, Thursday 22nd January 2015. “New Search Formulas for Computing Cuboids” . Click here for full text.
#59: A contribution to the Perfect Cuboid Problem. Submitted by Terry Raines, 9.30 GMT, Thursday 22nd January 2015. “Cuboid Miscellany” . Click here for full text.
#58: A contribution to the Perfect Cuboid Problem. Submitted by Robert D Matson, 8.00 GMT, Sunday 18th January 2015. “A suite of optimized computer programs was designed to systematically search for a perfect cuboid, ... While no perfect cuboid was found, the minimum length of the odd side has been substantially extended from the prior published limit of 3 trillion to 25 trillion...”. Click here for full text.
#57: A contribution to the Infinity of Fibonacci Primes. Submitted by Stephen Marshall 16.30 GMT, Saturday 17th January 2015. “This paper presents a complete and exhaustive proof that an infinite number of Fibonacci Primes exist ....”. Click here for full text.
#56: A contribution to the Polignac Prime Conjecture, Goldbach Conjecture, and Twin Primes Conjecture. Submitted by Stephen Marshall 16.30 GMT, Saturday 17th January 2015. “This paper presents a complete and exhaustive proof of the Polignac Prime Conjecture. The approach to this proof uses same logic that Euclid used to prove there are an infinite number of prime numbers”. Click here for full text.
#55: A contribution to the Perfect Cuboid Problem. Submitted by Scott Hampton, 2.30 GMT, Thursday 14th January 2015. “This paper will conclusively demonstrate that perfect cuboids do not exist” . Click here for full text.
#54: A contribution to the Perfect Cuboid Problem. Submitted by Jürgen Buchmüller 16.30 GMT, Friday 19th December 2014. “There can be no solution for a perfect cuboid in the pPT…” Click here for full text.
#53: A contribution to the Perfect Cuboid Problem. Submitted by John Ramsden 11.15 GMT, Thursday 20th November 2014. “We show by finding an explicit parametrization that a 4th degree surface which arises as a necessary condition for the existence of a perfect cuboid is a rational surface, i. e. birationally equivalent over Q to a plane.” Click here for full text.
#52: A contribution to the Collatz Conjecture. Submitted by Martiros Khurshudyan 12.30 GMT, Tuesday 18th November 2014. “Now we would like to consider (b; k; c; d; n) numbers such that the following holds …. (t)his generalization contains the Collatz problem as the partial case.” Click here for full text.
#51: A contribution to the Riemann Hypothesis. Submitted by Khalid Ibrahim 21.30 GMT, Wednesday 5th November 2014. “In this paper, we have established a connection between the Dirichlet series with the Mobius function and a functional representation of the zeta function in terms of its partial Euler product...” Click here for full text.
#47: A contribution to the Twin Primes Conjecture. Submitted by Ramón Ruiz Zapata 21.00 GMT, Sunday 21st September 2014. Click here for full text.
#46: A contribution to the Goldbach Conjecture. Submitted by Ramón Ruiz Zapata 21.00 GMT, Sunday 21st September 2014. “Initially, to prove this conjecture, we can form two arithmetic sequences (A and B) different for each even number, with all the natural numbers that can be primes, that can added, in pairs, result in the corresponding even number…” Click here for full text.
#44: A contribution to the Odd Perfect Number problem. First submitted by Peter Duval, 19.30 GMT, Tuesday 2nd September 2014, updated Friday 26th September 2014,and updated again Tuesday 21st October 2014. Click here for full text
#43: A contribution to the DLP and Diffie-Hellman problems. Submitted by Daniel Flatow, 00.30 GMT, Thursday 1st May 2014. Click here for full text
#42: A contribution to Fermat’s Last Theorem. Submitted by Peter Lesala, 17.30 GMT, Friday 4th April 2014. Click here for full text
#41: A contribution to the Perfect Cuboid Problem. Submitted by Robert D Matson, 8.00 GMT, Wednesday 2nd April 2014. “... the minimum length of the odd side has been extended from the prior published limit of 3 trillion (3 x 10
#38: A contribution to the Beal Conjecture. Submitted by Raj C Thiagarajan, 8.30 GMT, Friday 28th March 2014. “...we provide computational results and a proof for Beal’s conjecture. We demonstrate that the common prime factor is intrinsic to this conjecture using the laws of powers. Click here for full text.
#37: A contribution to the Legendre Conjecture. Submitted by A.Garcés Doz, 23.30 GMT, Tuesday 25th March 2014. “... a proof of this conjecture is presented, using the method of generating prime numbers between consecutive squares, and proving that for every pair of consecutive squares with n = 3 may be generated at least one prime number that belongs to the interval [n; (n + 1)
#36: Revisions to the solution to the Dorabella Cipher. Submitted by Tim Roberts, 15.00 GMT, Friday 7th March 2014. Click here for a brief version of the paper, describing both the decrypted text and the key, and click here for a newly revised version of the full paper.
#31: A contribution to the Riemann Hypothesis. Submitted by Kairbek Kazbekov, 11.00 GMT, Monday 2nd September 2013. “Horizontal and vertical distributions of complex zeros of the Riemann zeta-function in the critical region are being found in general form … on the basis of standard methods of function theory of complex variable.” Click here for full text.
#30: A contribution to the Riemann Hypothesis. Submitted by Cristian Dumitrescu 16.30 GMT, Tuesday 18th June 2013. “… ZFC cannot say much about a Turing machine that takes a very long time to halt (if it eventually halts)….” Click here for full text.
#26: A contribution to the Perfect Cuboid problem. Submitted by Tim Roberts, 01.30 GMT, Saturday 15th December 2012. Lists of primitive body cuboids (Euler bricks), edge cuboids, and face cuboids.
Contributions are removed after three years, unless specifically requested by the author.
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