This is false when the sum of 1/a + 1/b + 1/c < 1. The set of available sums < N is less than the product of the possible x,y,z values, N^(1/a) * N(1/b) * N^(1/c), so the average spacing is at least N ^ ( 1 - 1/a - 1/b - 1/c). The interesting cases are abc = 22* 233 234 235 236 244 333. Rich -----Original Message----- From: math-fun-bounces+rschroe=sandia.gov@mailman.xmission.com on behalf of David Wilson Sent: Sun 10/16/2005 1:17 PM To: Math-Fun; Sequence Fans Subject: [math-fun] Power Sum Conjecture I have very little evidence to believe this, but i'll put it forward anyway For a,b,c >= 2, x,y,z >= 0, the gap between numbers of the form x^a + y^b + z^c is bounded. -------------------------------- - David Wilson _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun