[math-fun] Generalized "square pyramid" question

Since 1^2 + 2^2 + 3^2 + ... + n^2 = Q^2 has only one nontrivial solution, I wonder what the prognosis is for exponents k higher than 2: QUESTION: For which k does there exist any nontrivial solution (n,Q) to 1^k + 2^k + 3^k + ... + n^k = Q^k ??? In particular, are there any solutions at all for k > 2 ? If so, what is the cardinality of the set of k for which solutions exist? (In particular, is it finite?) --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele