Type: Article

Generalized balancing numbers

Kálmán Liptai; Florian Luca; Akos Pintér; László Szalay;

Abstract:

The positive integer x is a (k. l)-balancing number for y (x <= y - 2) if l(k) + 2(k) + ... + (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.