Counterexample found by Lander & Parkin in 1966: 27^5 + 84^5 + 110^5 + 133^5 = 144^5 http://en.wikipedia.org/wiki/Euler%27s_sum_of_powers_conjecture http://mathworld.wolfram.com/EulersSumofPowersConjecture.html http://euler.free.fr/index.htm Christian. -----Message d'origine----- De : math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] De la part de David Makin Envoyé : lundi 12 novembre 2012 13:30 À : math-fun Objet : [math-fun] Fermat's last theorem Hi, Just a quick thought I had the other day, as I understand it Fermat's last theorem (now proved) basically says that for: a^p + b^p = c^p Then where all variables are integers there are no solutions for a, b and c where p>2. My thought was has anyone considered: a^p + b^p + c^p = d^p or indeed: a1^p + a2^p + a3^p + ..... an^p = b^p And is it possible that for the case of: a^p + b^p + c^p = d^p Then there is a solution for a,b,c,d for p=3 but not for p>3 and generally for: a1^p + a2^p + a3^p + ..... an^p = b^p there's a solution for a1..an and b if p=n but not for p>n ? _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun