User:Sinhacon/Sinha Conjecture Prize

Sinha Conjecture
Here is the more descriptive form of the Sinha Conjecture:

Let X, Y, Z, a, b, and c be positive integers, with a, b, $$c > 2$$. Whether X and Y have a common factor or not, the equation X a + Y b = Z c has a solution if:


 * X, Y and Z has a common factor, or


 * each of X and Y separately has a common factor with Z, when X and Y coprime, or


 * at least any one of X and Y is coprime with Z, when X and Y coprime;

and the equation X a + Y b = Z c has no solution if:


 * X, Y and Z coprime, or


 * each of X and Y separately coprime with Z, when X and Y has a common factor, or


 * at least any one of X and Y is coprime with Z, when X and Y have a common factor.

Background
Andrew Beal, a Dallas banker and another non-mathematician, has formulated a conjecture, known as Beal Conjecture, which generalised the Fermat's last theorem (FLT). The definition of Beal Conjecture is quite simple in respect to Sinha's Conjecture. Beal has found only two possibilities of FLT. But the original picture is very complicated with a set of eight possibilities. Like Beal, Sinha also believes that, perhaps, Fermat has a proof, or at least a hint of proof, for his last theorem. So, first of all, Sinha tried to solve the Beal Conjecture and found the proof of Beal Conjecture, which immediately succeeded to gain two additional conjectures, more precisely, the Sinha Conjecture. This conjecture is more complex and challenging than Beal's earlier proposal. Sinha is never going to claim the Beal Conjecture Prize awarding money ever. He believes, if his proof leads us into a complicated conjecture then the Beal Conjecture, then other attempts to proof the Beal Conjecture must lead us into more deep inside of FLT in future. Money is priceless before the research and future developments of our knowledge, he believes.

Sinha Conjecture Prize
Excogitation & Innovation Laboratory has announced an award of US $150,000.00 in June 9, 2009 (the award money is made triple in January 11, 2010), for the proof or disproof of the Sinha Conjecture.

Terms and Conditions
In awarding the prize no consideration whatever will be given to the nationality, genders, or races, of the candidates, but that the most worthy will receive the prize. Competence to submit proposals for the award of prize will be enjoyed by anyone. Any proof or disproof must be appeared in a reputable refereed journal. The Prize-awarding Committee will take a final decision after two years from the date of publication of a certain proposal. During this two-year period, a group of three to five eminent Number Theorists will review the proposal and give their opinion in the matter of the award of prize. The deliberations, opinions and proposals of the award of prize may not be made public, generally. If there is a conflict, the problem will be solved under the Indian Court of Justice. For multiple proposals, the prize will be awarded to the first proposal only. The Prize may be equally divided between two works each of which may be considered to merit a prize. Has a work, which is to be rewarded, been produced by two or more persons, the prize will be awarded to them jointly. The awarding money will be declared to the first author's name of each paper.

If you have questions, they can be mailed to:

Director Excogitation & Innovation Laboratory 45/2, Atul Prasad Sarani, Hakimpara, P.O. Rabindra Sarani, Siliguri, W.B. 734 006-05, India

Or, they can be e-mailed to: admin @ eilab.org (please, delete the empty spaces before and after the @ sign)

Who is Sinha
Neil Sinha is a Scientist in E.I. Laboratory and also chairs as the CEO of Sinha Inc. -- his own company. Before he has founded Sinha Inc., he has worked as a Sales Officer, a Sales Manager, a Marketing Manager in various companies, and lastly, as the Director of E.I. Laboratory.

After completing his Graduate Degree in Biological Sciences (North Bengal University), he found himself under increasing pressure to develop a work in the Quantum Gravitation. But it was a painstaking research to find an Quantum equation for the Einstein's relativity (see Complete Relativity ). In the meanwhile, he was interested in Number Theory as well, basically in his all-time favourite Fermat's works. Andrew Beal, a Dallas banker (another non-mathematician), has formulated a conjecture, known as Beal Conjecture, which generalised the Fermat's last theorem (FLT). Sinha tried to solve the Beal Conjecture and after a conscientious research, he found the proof of Beal Conjecture. It was his uncompromising passion that brings us into an additional conjecture apart from Beal's earlier proposal, more precisely, known as the Sinha Conjecture. This conjecture is more complex and challenging than the Beal Conjecture. The definition of Beal Conjecture is quite simple in respect to the Sinha's Conjecture.

Apart from his ongoing research on Quantum Gravity and Particle Interactions, presently, Sinha (a former member of SAE, USA) is also designing a high-efficient automotive engine as well as a low cost thermonuclear reactor.

Sinha loves to write. He won some local-awards for his poetries, short stories and essays (including one from the Government of West Bengal). He is as well a songwriter and a movie scriptwriter.

See Sinha's original article, please, click: The Conjecture.