Erd\H{o}s-Moser Equation in Arithmetic Progressions

Anji Dong; Vi Anh Nguyen; Alexandru Zaharescu

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arXiv · 2608.03375

Erd\H{o}s-Moser Equation in Arithmetic Progressions

Anji Dong·Vi Anh Nguyen·Alexandru Zaharescu

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Abstract

We consider the Erd\H{o}s-Moser equation $1^k+2^k+\cdots+(m-1)^k=m^k$ in arithmetic progressions. We prove among other things that when $k=2$, for any solution to exist, the above sum in arithmetic progression must consist of two or four terms. In either case, there are infinitely many solutions that can be completely characterized.

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Anji Dong, Vi Anh Nguyen, Alexandru Zaharescu. 2026-08-04. Erd\H{o}s-Moser Equation in Arithmetic Progressions. https://arxiv.org/abs/2608.03375

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