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arXiv · 1003.1646

On stronger conjectures that imply the Erdös-Moser conjecture

Bernd C. Kellner
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Abstract

The Erdös-Moser conjecture states that the Diophantine equation $S_k(m) = m^k$, where $S_k(m)=1^k+2^k+...+(m-1)^k$, has no solution for positive integers $k$ and $m$ with $k \geq 2$. We show that stronger conjectures about consecutive values of the function $S_k$, that seem to be more naturally, imply the Erdös-Moser conjecture.

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Bernd C. Kellner. 2012-09-05. On stronger conjectures that imply the Erdös-Moser conjecture. https://doi.org/10.1016/j.jnt.2011.01.004

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