![MillionCube.jpg](https://steemitimages.com/DQmVX5zzJU7Fs46sVBCGP51bKAVftAVPw3jVm8QAcqGMT77/MillionCube.jpg) 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! 🐟 ..................... 🐳 --- --- Have fun with this. Good Luck to all.