Re: [math-fun] x^n + y^n = z^n + w^n

Christian Boyer wrote:

Jean-Charles Meyrignac thinks that a^n + b^n = c^n + d^n, with n>4, is impossible.

On a^5 + b^5 = c^5 + d^5 + e^5, he says that the ONLY known solution is 14132^5 + 220^5 = 14068^5 + 6237^5 + 5027^5 = 563661204304422162432 So, for sure, it will be incredibly difficult to find solutions with e=0.

The first counterexample to a conjecture of Euler was 84^5+110^5=144^5+(-27)^5+(-133)^5. Do you want solutions in the integers or in the positive integers? Gary McGuire