Mathematical question relating to Fermat's last theorem

[hiflier]

Fermat's theorem stated that there was no whole number solution to the equation a^n+b^n=c^n where n was any whole number greater than 2. But has anyone investigated the possibility of a solution to the equation a^n+b^n+c^n...+n^n=m^n? (The symbol ^ meaning 'to the power of'.)

[KerrAvon]

yes that is also FLT, the subsequent stages can be reduced to the current equation.

[bert_h]

Sorry, your equation is unrelated to Fermat's equation. The best resource on the web is Mathworld Wolfram, and it has some remarks on sums of three integer cubes under "Waring's Problem". There is also an interesting page:
http://mathworld.wolf...quation4thPowers.html
which explains (I think!) that there are infinite families of integer solutions to a^4 + b^4 + c^4 = n^4. So yes, such equations are studied, but there doesn't seem to be much in the way of a general result - each exponent behaves differently from the others.

[LazyGun]

Naah, has to be hollow - this site says so, in yellow text on a black background, so it must be true :)

http://www.ourhollowearth.com/

[LazyGun]

doh- posted in error - ignore ;)