Ricardo,

Does someone in the list know if the following conjecture, that includes as a particular case Fermat's Last Theorem, has ever been posed, and proved false or true? x[1]^p + x[2]^p + ... x[n]^p = z^p, for x[i] > 0 and 1 < n < p, has no integer solutions. TIA.

Yes, this conjecture was made by Euler in 1769. He conjectured "it is impossible to exhibit three fourth powers whose sum is a fourth power, four fifth powers whose sum is a fifth power, and similarly for higher powers." This was first disproven in 1966 by L.J.Lander & T.R.Parkin with: 27^5+84^5+110^5+133^5 =144^5 The first found with fourth powers was done by Noam Elkies in 1988 and is: 20615673^4 = 2682440^4 + 15365639^4 + 18796760^4 Then Roger Frye found: 422481^4 = 95800^4 + 217519^4 + 414560^4 which is the smallest solution for fourth powers. From, Rupert _________________________________________________________________ Chat with friends online, try MSN Messenger: http://messenger.msn.com