Main post link -> http://newsfeed.time.com/2013/06/11/solve-this-math-problem-win-a-million-bucks/?hpt=hp_t3

We know many of you are into Fermat's last theorem and thought you might be interested in the Beal Conjecture as well. Expanding the frontier of number theory probably isn't the easiest way to make a million bucks, or even the best reason to work on that kind of problem. That is an impressive prize though, here is the prize page from the American Mathematical Society.

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TopNewestThere are 6(originally 7) unsolved conjectures known as the millennium prize problems and for solving each,the Clay Mathematical Institution offers a million bucks.The Poincare Conjecture is the only one that has been proved. – Edward Elric · 4 years, 1 month ago

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– Aditya Parson · 4 years, 1 month ago

what if gcd(a,b) is 1?Log in to reply

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– Aditya Parson · 4 years, 1 month ago

Prove/ Disprove. The conjecture has to be proved first, to eliminate the possibility that \(gcd(A,B) \neq 1\). And if this equation also satisfies for \(gcd(A,B)=1\), then \(gcd(A,B,C)\) will of course be \(1\). So, you have to prove that the equation is not satisfied for any pair of CO-PRIME integers.Log in to reply

Wait maybe we can use fermat's little theorem to turn it into a more simpler problem.. – Taehyung Kim · 4 years, 1 month ago

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Maybe Fermat proved his last theorem using the Beal equation? (see if you can find out how) – Taehyung Kim · 4 years, 1 month ago

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thanks a lot for giving such a great problem i'll surely give it a try – Tejas Kasetty · 4 years, 1 month ago

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Similarly play around with the equation and it will be apparent that the equation will not hold for set of primes. – Aditya Parson · 4 years, 1 month ago

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– Aditya Parson · 4 years, 1 month ago

I already said that it will not hold if you take prime numbers greater than 2. I just gave you the simplest way to prove it.Log in to reply

– Shivang Jindal · 4 years, 1 month ago

Ok then prove it :DLog in to reply

– Aditya Parson · 4 years, 1 month ago

\(A,B,C\) can be co-prime as well. The equation will not hold if all \(3\) are primes. As such, we still need to prove that this equation is valid/not valid when if \(A,B,C\) are co-prime. Then we can conclude if there is a common factor of the three terms or not.Log in to reply

– Aditya Parson · 4 years, 1 month ago

Also, there are cases when \(A,B,C\) are equal to \(2\) There is still a lot of work to be done to prove/disprove this equation.Log in to reply

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– Aditya Parson · 4 years, 1 month ago

Yes, that is again a part of it which you proved.Log in to reply

just read how technical the proof of fermats last theorem by andrew willes first before someone considers your boring proof!!! – Mharfe Micaroz · 4 years, 1 month ago

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