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Un milione di dollari per voi se risolverete questo problema, pubblicato sul sito dell'American Mathematical Society:

Beal Prize Conjecture
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.
[By way of example, 3³ + 6³ = 3⁵, but the numbers that are the bases have a common factor of 3, so the equation does not disprove the theorem; it is not a counterexample.]