Erdős-Moser Equation in Arithmetic Progressions
Anji Dong, Vi Anh Nguyen, Alexandru Zaharescu
Abstract
We consider the Erdős-Moser equation 1k+2k+·s+(m-1)k=mk 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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