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.

 

 

#66: A contribution to the Magic Square of Squares ProblemSubmitted 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 ProblemSubmitted 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 ProblemSubmitted by Terry Raines, 17.30 GMT, Friday 20th March 2015. 

“Cuboid Parametric Formulas” .  Click here for full text.

 

#63: A contribution to the Legendre ConjectureSubmitted 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 ProblemSubmitted 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 ProblemSubmitted 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 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.

 

#57: A contribution to the Infinity of Fibonacci PrimesSubmitted 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 ConjectureSubmitted 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 ProblemSubmitted 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 ProblemSubmitted 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 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.

 

#49: A contribution to both the Legendre and Goldbach ConjecturesSubmitted by Jamel Ghanouchi, 22.45 GMT, Wednesday 1st October 2014.

“In this document, we deal with the concept of prime number together with the Legendre and Goldbach conjectures…”  Click here for full text.

 

#48: A contribution to the Twin Primes ConjectureSubmitted by Takasugi Touichi 11.00 GMT, Tuesday 30th September 2014.

“Twin primes conjecture….is in the same root of Riemann hypothesis….(t)he prime number is the base of time...”  Click here for full text. 

 

#47: A contribution to the Twin Primes ConjectureSubmitted by Ramón Ruiz Zapata 21.00 GMT, Sunday 21st September 2014.

Click here for full text. 

 

#46: A contribution to the Goldbach ConjectureSubmitted 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 problemFirst 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 problemsSubmitted by Daniel Flatow, 00.30 GMT, Thursday 1st May 2014. 

Click here for full text

 

#42: A contribution to Fermat’s Last TheoremSubmitted by Peter Lesala, 17.30 GMT, Friday 4th April 2014. 

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

 

#38: A contribution to the Beal ConjectureSubmitted 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 ConjectureSubmitted 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)2]”. 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.

 

#35: A contribution to the Perfect Cuboid problemSubmitted by Conor Williams, 2.00 GMT, Tuesday 4th March 2014.  Revised version submitted Wednesday 12th March 2014.

“...the proof boils down to whether the sides are even or odd...“.  Click here for full text.

 

#34: A contribution to the Rational Distance problemSubmitted by Conor Williams, 1.30 GMT, Tuesday 25th February 2014.  Revised version submitted Wednesday 12th March 2014.

“...Z cannot be a perfect square root...which means L cannot be rational and if it cannot be rational then P cannot exist given the initial conditions... . Click here for full text.

 

#31: A contribution to the Riemann HypothesisSubmitted 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 HypothesisSubmitted 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.

 

#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 requested by the author.  

 

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Tim S Roberts

Email: timro21@gmail.com