UNSOLVED PROBLEMS

In Number Theory, Logic, and Cryptography

Solutions

 

This page provides a means for authors to have their proposed solutions published.  Details will include the name and email address of the author, and the date and time of first submission.

 

#01: Submitted by Jeffrey Cook, 23.00 GMT, Wednesday 23rd May 2007.

 

A proposed proof of the Riemann Hypothesis. 

 

I introduce a function useful for defining any random or seemingly random values whether involving figures divided by zero, undefined and infinite limits of both real and imaginary numbers. With this function and a number of related, provable theorems, it is shown that the Riemann Hypothesis is true and brings into play the notion put forth by Jordan that a simple closed curve contains two discontinuous regions—an inside and an outside...  Click here for full text.

 

 

#02: Submitted by George Hoschel Jr., 3.30 GMT, Tuesday 1st May 2007.

 

A proposed solution to the Dorabella Cipher. 

 

"Oh, has P. dub belle you? Gee, I'd dub belle you..."  Click here for full text.

 

 

#03: Submitted by Greg Orme, 9.45 GMT, Thursday 24th May 2007 , updated 12th December 2009.

 

A proposed proof of the Riemann Hypothesis. 

 

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.

 

 

#04: Submitted by Tony Gaffney, 1.00 GMT, Thursday 5th July 2007.

 

A proposed solution to the Dorabella Cipher. 

 

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

 

 

#05: Submitted by Tim Roberts, 15.00 GMT, Tuesday 29th January 2008.

 

A contribution to the Odd Perfect Number problem. 

 

"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.

 

 

#06: Submitted by Sylvain Julien, and Quentin Guignard 13.00 GMT, Thursday 1st January 2009.

 

A proposed solution to the Goldbach Conjecture. 

 

"Consider a composite natural number n greater or equal to 4. We aim at proving that there is at least one natural number r such as (n-r) and (n+r) are both primes. For obvious reasons r<n-2. Such a number r will be called a "primality radius" of n..."  Click here for full text.

 

 

#07: Submitted by Vernon H Graves 10.30 GMT, Friday 9th January 2009.

 

A proposed disproof of the existence of an Euler Brick. 

 

IMPORTANT NOTE: the author acknowledges a significant error in the main proof.  However, the solution as provided is still presented here in the hope that the lines of reasoning may inspire others.   Click here for full text.

 

 

#08: Submitted by Nafets Azereb 10.30 GMT, Thursday 12th March 2009.

 

A proposed disproof of the existence of an odd perfect number. 

 

“All consecutive odd numbers (from 1) added together form always a square.  Imagine a square x^2 built by odd numbers (added together) from 1 to F[g]…”.   Click here for full text.

 

 

#09: Submitted by George Hoschel Jr., 18.30 GMT, Wednesday 25th March 2009.

 

A proposed solution to the Voynich Manuscript. 

 

Five pages: page 1, page 2, page 3, page 4, page 5.

 

 

#10: Submitted by Nafets Azereb 3.30 GMT, Tuesday 31st March 2009.

 

A proposed disproof of the existence of a perfect Euler Brick. 

 

“Rules for the integral rectangular triangles [Pythagorean triangles] have been established since time of Diophantus…”.   Click here for full text.

 

 

#11: Submitted by Nafets Azereb 10.30 GMT, Thursday 9th April 2009.

 

A proposed proof of the Goldbach Conjecture. 

 

“Assume there is (or are) numbers that defy the Conjecture; call them even[d].…”.   Click here for full text.

 

 

#12: Submitted by Tim Roberts, 15.00 GMT, Sunday 24th May 2009.

 

The solution to the Dorabella Cipher. 

 

"P.S. Now droop beige weeds…. "  Click here for the solution.

 

 

#13: Submitted by Tom Milner-Gulland, 23.30 GMT, Monday 17th August 2009.

 

A possible solution to the Goldbach and Twin Prime Conjectures. 

 

"Our approach is concerned with total numbers of divisors of integers in specified intervals…”.  Click here for full text. 

 

 

#14: Submitted by Don Blazys, 22.30 GMT, Tuesday 15th December 2009.

 

A possible solution to the Beal Conjecture. 

 

"In this paper, 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. 

 

 

#15: Submitted by John Milmore , 11.30 GMT, Thursday 11th March 2010.

 

A contribution to the RSA Challenge. 

 

"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. 

 

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