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Divisibility of power sums and the generalized Erdős-Moser equation. (English) Zbl 1264.11025
For k an integer, let ν 2 (k) denote the highest exponent ν such that 2 ν divides k. Given positive integers m and n the authors relate, using induction, ν 2 (1 n +2 n ++m n ) to ν 2 (m(m+1)/2). They apply this result to give an easy reproof of the result of the reviewer [Bull. Aust. Math. Soc. 53, No. 2, 281–292 (1996; Zbl 0851.11020)] that if 1 n +2 n ++(m-1) n =am n , then m must be odd.
11D41Higher degree diophantine equations