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 Ax + By = Cz where x, y and z are all positive integers greater than 2.
This is called the Beal Conjecture which is still unproven:
If Ax + By = Cz, 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)
Some more examples of almost winners:
The official rules and how to submit your winning solution:
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.