Generalized balancing numbers

The positive integer x is a (k, l) -balancing number for y(x ≤ y - 2) if 1k + 2k + ... + (x - 1)k = (x + 1)l + ... + (y - 1)l for fixed positive integers k and l. In this paper, we prove some effective and ineffective finiteness statements for the balancing numbers, using certain Baker-type Diophantine results and Bilu-Tichy theorem, respectively. © 2009 Royal Netherlands Academy of Arts and Sciences. All rights reserved.