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

David wrote:

I don't recall ever hearing of a solution to a_1^k +- a_2^k +- a_3^k +- ... +- a_j^k = 0 in distinct positive integers a_i with 1 <= j < k.

Yes, you are right. My question is specifically on (j,k)=(4,>4): what are the already checked ranges of integers? Only Blair Kelly's results? x^5 + y^5 < 1.02 x 10^26 means a not very large range: 0 < x < y < 160,000. I will ask Jean-Charles Meyrignac, http://euler.free.fr/, he has perhaps some answers. Christian.