Results computed by Stuart Gascoigne, some months ago: no solution x^5 + y^5 = z^5 + w^5 < 3.26 x 10^32. Means x,y,z,w < ~3,200,000. A larger range than the Blair Kelly's range x,y,z,w < ~160,000. Solutions to x^n + y^n = z^n + w^n with n>4 looks so unlikely... But a proof of the impossibility of this extension -"only" adding w^n- to the Fermat's last theorem looks also unreachable. I would like to know the feeling of Andrew Wiles on this question. Christian. -----Message d'origine----- De : math-fun-bounces+cboyer=club-internet.fr@mailman.xmission.com [mailto:math-fun-bounces+cboyer=club-internet.fr@mailman.xmission.com] De la part de Christian Boyer Envoyé : vendredi 16 juin 2006 11:38 À : math-fun@mailman.xmission.com Objet : [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. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun