hihi, all - ok, i have run the program to find solutions to n = a^2 + b^3 + c^4 + d^5 + e^6 for non-negative n and a, b, c, d, e at least s, for s=2 up to n=336807, for s=1 up to n=100000, and for s=0 (the usual problem statement) up to n=404219 the program prints for each n how many representations there are (and a flag can be set to print them also, but i didn't do that) the program for s=0 took about 48 hours, and the time complexity appears to be roughly quadratic i plotted the growth of the number of solutions, and it appears to be much less than linear, but with very wide variation - i don't really have time to do the data analysis, but i'd be happy to send the output file to anyone who wants it (it is a little over 4MB, or 1.4MB as a gzipped tar file - this is just the s=0 output, which i gather is the most interesting, though the others have very similar shapes) more soon, cal