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. ----- Original Message ----- From: "Christian Boyer" <cboyer@club-internet.fr> To: <math-fun@mailman.xmission.com> Sent: Friday, June 16, 2006 5:38 AM Subject: [math-fun] x^n + y^n = z^n + w^n
We know integer solutions of x^n + y^n = z^n + w^n, for n <= 4. For example, for n=4: http://www.research.att.com/~njas/sequences/A018786
But it seems that we do not know any nontrivial solution for n > 4. Am I right?
Blair Kelly found no solution for x^5 + y^5 = z^5 + w^5 < N = 1.02 x 10^26 (Guy's UPINT, 3rd edition, p.210). Do you know some other results for n > 4?
Christian.
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