UNSOLVED PROBLEMS

In Number Theory, Logic, and Cryptography

Proposed 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.

 

#23: A contribution to the Beal Conjecture. Submitted by Zurab Pavlenishvili, 9.30 GMT, Monday 23rd April 2012.

 

Removed at the request of the author.

 

 

#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.

 

 

#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. 

 

 

#13: A contribution to the Goldbach and Twin Prime Conjectures. Submitted by Tom Milner-Gulland, 23.30 GMT, Monday 17th August 2009.

 

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

 

 

#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, here for a brief summary, and here for a layman’s mathematical justification of correctness.

 

 

#09: A proposed solution to the Voynich Manuscript. Submitted by George Hoschel Jr., 18.30 GMT, Wednesday 25th March 2009.

 

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

 

 

#08: A proposed disproof of the existence of an Odd Perfect Number. Submitted by Nafets Azereb 10.30 GMT, Thursday 12th March 2009.

 

“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.

 

 

#06: A contribution to the Goldbach Conjecture. Submitted by Sylvain Julien, 13.00 GMT, Thursday 1st January 2009.

 

"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.

 

 

#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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