Very interesting, Richard -- and Ed ! This suggests a few questions to me, possible hard ones: 1) Can we prove there are infinitely many solutions to T[x] + T[y] = z! ? How about a probabilistic heuristic? 2) Generally, given reasonably simple functions F,G: Z+ -> Z+ when can we prove there are infinitely many solutions to F(x) + F(y) = G(z) ? Likewise, what about a probabilistic "proof" ? --Dan ---------------------------------------------- Richard wrote: << . . . Solutions of x(x+1)/2 + y(y+1)/2 = z! are solutions of (2x+1)^2 + (2y+1)^2 = 8(z!) + 2 and the first few values of z for which there are solutions can easily be ascertained: (x,y,z) = (0,1,0), (0,1,1), (1,1,2), (0,3,3), (2,2,3), (2,6,4), (0,15,5), (5,14,5), (45,89,7), (89,269,8), (210,825,9), (760,2610,10), (1770,2030,10), . . .
_____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele