Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4673262 | Indagationes Mathematicae | 2009 | 14 Pages |
Abstract
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.
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