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.

 

 

#83:  A contribution to the Perfect Cuboid Problem. Submitted by Lee Morgenstern21.00 GMT, Thursday 24th March 2016.

A new approach is given …. proving many special cases impossible using inequality relationships…”   Click here for full text.

 

#74: A contribution to the Collatz ConjectureSubmitted 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 ProblemSubmitted 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 ProblemSubmitted 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 CipherSubmitted 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.

 

#60: A contribution to the Perfect Cuboid ProblemSubmitted 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 ProblemSubmitted by Terry Raines, 9.30 GMT, Thursday 22nd January 2015.

“Cuboid Miscellany” .  Click here for full text.

 

#58: A contribution to the Perfect Cuboid ProblemSubmitted 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.

 

#53: A contribution to the Perfect Cuboid ProblemSubmitted 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 ConjectureSubmitted 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 HypothesisSubmitted 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.

 

#41: A contribution to the Perfect Cuboid ProblemSubmitted 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 1012) to 8 trillion (8 x 1012).”  Click here for full text

 

#36: Revisions to the solution to the Dorabella CipherSubmitted 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.

 

#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.

 

#14: A contribution to the Beal ConjectureSubmitted by Don Blazys, 22.30 GMT, Tuesday 15th December 2009.

"...we present a newly discovered logarithmic identity whose properties demonstrate that division by zero prevents the substitution of identities if and only if it is assumed that “Beal’s Conjecture” is false.”  Click here for full text, and here for a more abbreviated version. 

 

Contributions are removed after three years, unless specifically agreed by the developer and the author.  

 

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Tim S Roberts

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