Yes, that was conjectured, but Noam Elkies found a counter-example (four fifth powers in the relationship a^5 + b^5 + c^5 = d^5, or something like that). Sincerely, Adam P. Goucher

----- Original Message ----- From: David Makin Sent: 11/12/12 12:29 PM To: math-fun Subject: [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