UNSOLVED PROBLEMS

In Number Theory, Logic, and Cryptography

Contributions and Proposed Solutions

 

This page provides a means for authors to have their proposed solutions made available for open inspection and feedback. 

Contributions are as supplied by the author, and are not peer-reviewed.  Constructive feedback is encouraged, and should be sent direct to the relevant author. 

 

 

#33: A small revision to the solution to the Dorabella Cipher. Submitted by Tim Roberts, 15.00 GMT, Sunday 13th October 2013.

 

Click here for a brief version of the paper describing the decrypted text and the key.

 

 

#32: A contribution to the Riemann Hypothesis. Submitted by Jamel Ghanouchi, 21.00 GMT, Wednesday 2nd October 2013. 

 

“We present the Riemann problem and define the real primes. It allows to generalize the Riemann hypothesis to the reals. A calculus of integral solves the problem. We generalize the proof to the integers.” Click here for full text.

 

 

#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 in the paper 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. 

 

“In this article I describe a proof of the fact that ZFC cannot say much about a Turing machine that takes a very long time to halt (if it eventually halts). The consequences of this fact in relation to the Riemann Hypothesis are presented.” Click here for full text.

 

 

#27: A contribution to the Beal Conjecture. Submitted by Jamel Ghanouchi,  Latest revised version submitted 14.30 GMT, Monday 20th May 2013.

 

“We begin with Beal equation Z^c = X^a +Y^b and prove that it does not have solutions for both a > 2, b > 2 and c > 2 which is Beal conjecture.  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..

 

 

#22: A contribution to the Collatz Conjecture. Submitted by Steffen Bode, 16.30 GMT, Monday 3rd October 2011.

 

"I establish the existence of a unique binary pattern inherent to the 3n+1 step, and then use this binary pattern to prove the 3n+1 problem for all positive integers.”  Click here for full text.

 

 

#21: A contribution to the Pillai and Fermat-Catalan Conjectures. Submitted by Jamel Ghanouchi, 11.00 GMT, Thursday 22nd September 2011, most recent revised version (in French) submitted Saturday 9th March 2013.

 

“Nous commençons avec l’équation de Beal (ou Fermat-Catalan) U^c = X^a+Y^b puis nous definissons deux équations qui en sont conséquentes. Après en avoir déduit quelques résultats, nous généralisons l’approche à toutes les équations de Fermat-Catalan ; ce qui nous permet de relier le problem au théorème de Matyasevitch.”  Click here for full text

 

 

#20: A contribution to the Goldbach Conjecture. Submitted by Jamel Ghanouchi, 11.00 GMT, Thursday 22nd September 2011.

 

“We define the primal radius : For all x an integer greater or equal to 3, we define a primal number r for which x - r and x + r are prime numbers.”. Click here for full text.

 

 

#19: A contribution to the Goldbach Conjecture. Submitted by William Brookfield, 23.00 GMT, Saturday 27th August 2011.

 

"I am here proposing that the validity of the Goldbach conjecture is axiomatic to the number system itself...”.  Click here for full text.

 

 

#18: A contribution to the Odd Perfect Number problem. Submitted by Arian Berdellima , 10.00 GMT, Wednesday 8th June 2011 (original at the Munich Personal RePEc Archive).

 

"In this work we construct a lower bound for an odd perfect number in terms of the number of its distinct prime factors”.  Click here for full text.

 

 

#17: A contribution to number theory. Submitted by Marco Ripà, 21.15 GMT, Friday 18th March 2011.

 

"Patterns related to the Smarandache circular sequence primality problem ”.  Click here for full text.

 

 

#16: A contribution to the Odd Perfect Number problem. Submitted by Jose Arnaldo Dris, 7.15 GMT, Saturday 5th March 2011.

 

"Some New Results on Bounds for the Abundancy Indices of the Components of Odd Perfect Numbers”.  Click here for full text.

 

 

#15: A contribution to the RSA Challenge. Submitted by John Milmore , 11.30 GMT, Thursday 11th March 2010.

 

"An expansion of Fermat's conjecture that any composite is the difference

between two squares yields a factoring methodology that is obviously more

computer efficient than the "Sieve of Eratosthenes".  Click here for full text. 

 

 

#14: A contribution to the Beal Conjecture. Submitted 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. 

 

 

#12: The solution to the Dorabella Cipher. Submitted by Tim Roberts, 15.00 GMT, Sunday 24th May 2009.

 

"P.S. Now droop beige weeds…. "  Click here for a paper describing the decryption.

 

 

#05: A contribution to the Odd Perfect Number problem. Submitted by Tim Roberts, 15.00 GMT, Tuesday 29th January 2008.

 

"It has been known since the time of Euler that an odd perfect number N (if it exists) must have the form N = p^aQ²... "  Click here for full text.

 

 

#04: A proposed solution to the Dorabella Cipher. Submitted by Tony Gaffney, 1.00 GMT, Thursday 5th July 2007.

 

"B (Bella) hellcat i.e. war using...."  Click here for full text.

 

 

#03: A proposed proof of the Riemann Hypothesis. Submitted by Greg Orme, 9.45 GMT, Thursday 24th May 2007 , updated 12th December 2009.

 

“The aim of the proof is first to demonstrate that selecting N random numbers, as shown by Reuben and Hersh, that there is an equal chance of selecting a number with an odd or even number of factors. Then the aim is to show that this also applies from 1 to N…”  Click here for full text.

 

 

Some contributions previously appearing on this site have been removed at the request of the authors.

 

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This web site developed and maintained by

Tim S Roberts

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