Sinha Conjecture Prize

The Sinha Conjecture Prize in Number Theory is an award announced by the Excogitation & Innovation Laboratory on June 9, 2009, amounting to US$150,000, for the proof or disproof of a mathematical proposition the Laboratory calls the "Sinha Conjecture". The prior award money was US $50,000, and it was tripled on January 11, 2010.
Background
Andrew Beal, a Dallas banker and a number theory enthusiast, had formulated a conjecture, known as Beal's conjecture, which generalizes Fermat's last theorem (FLT). Similarly, the non-mathematician and physics enthusiast Neil Sinha proposed a different conjecture implying FLT. Here is the modified form of the conjecture:<ref name="EI" />

Let X, Y, Z, a, b, and c be positive integers, with a, b, c > 2. The equation X + Y = Z has a solution if:
* at least one of X or Y is coprime with Z, when X and Y have a common factor;
or,
* at least one of X or Y has a common factor with Z, when X and Y coprime.

Terms and conditions
In awarding the prize no consideration whatever will be given to the nationality, gender, or race, of the candidates, but that the most worthy will receive the prize. Anyone may submit proposals for the award of prize, but a proof or disproof must appear in a reputable refereed journal. The Prize-awarding Committee will take a final decision after two years from the date of publication of a proposal. During this two-year period, a group of three to five 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. Conflicts are resolved by 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. If a work which is to be rewarded has been produced by two or more people, the prize will be awarded to them jointly. The awarding money will be declared to the first author's name of each paper.
Note
The Sinha conjecture is closely related to Beal's conjecture. The modularity theorem is likely to have some bearing on Sinha conjecture.

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