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

Gary McGuire wrote

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?

Yes, positive distinct integers. About a^n = b^n + c^n + d^n + e^n, there is your solution: 144^5 = 133^5 + 110^5 + 84^5 + 27^5 but also this other one found by Jim Frye in 2004: 85359^5 = 85282^5 + 28969^5 + 3183^5 + 55^5 Christian.