Win 1 Million Dollars ($1,000,000) by solving this with positive integers that disprove the Beal Conjecture

Solve this and win USD $1,000,000

A^3 + B^3 = C^3 where positive integers A, B and C do not have a common prime factor.

There are even additional ways to win this Million Dollar prize:

You are not limited to only cubes. You can change the powers so that A^x + B^y = C^z where x, y and z are all positive integers greater than 2.

This is called the Beal Conjecture which is still unproven:

If A^x + B^y = C^z, where A, B, C, x, y and z are positive integers and x, y and z are all greater than 2, then A, B and C must have a common prime factor.

To win the $1 million dollar prize you can either prove it or disprove it by solving it, that is, give a counter example.

A counter example is just solving the equation with integers that do not have a common prime factor that would prove the Beal Conjecture to be false.

We can try A = 3 and B = 4 and x = y = z = 3 then 3³ = 27 and 4³ = 64 so that 27 + 64 = 91
But the cube root of 91 = 4.49794... is not an integer so that doesn't win.

Let's try A = 3 and B = 6 then 3³ + 6³ = 27 + 216 = 243 = 3⁵ = 3³ + 6³
Wow! I just won a million dollars ... almost.
The disqualifier is A, B and C have a common prime factor of 3

How about 1³ + 2³ = 3²
Although this is true, one of the exponents is 2 and therefore disqualified.

The Beal Conjecture was formulated by mathematician and banker, Andrew Beal in 1993. He started offering a reward for proving or disproving it twenty years ago. He has increased the reward a few times and it now stands at $1 Million Dollars USD.

The prize money is being held by the American Mathematical Society (AMS)

More info here:
http://www.ams.org/profession/prizes-awards/ams-supported/beal-prize

And here:
https://en.wikipedia.org/wiki/Beal_conjecture

Some more examples of almost winners:
http://www.ams.org/notices/199711/beal.pdf

The official rules and how to submit your winning solution:
http://www.ams.org/profession/prizes-awards/ams-supported/beal-prize-rules

If a steemian wins this prize, he or she can instantly become a whale, so be sure to resteem!

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Have fun with this.

Good Luck to all.