On stronger conjectures that imply the Erd\"os-Moser conjecture

Bernd C. Kellner

doi:10.1016/j.jnt.2011.01.004

On stronger conjectures that imply the Erd\"os-Moser conjecture

Number Theory 2012-09-06 v2

Authors: Bernd C. Kellner

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Abstract

The Erd\"os-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 Erd\"os-Moser conjecture.

Keywords

erdős-moser conjecture diophantine equation sum of powers consecutive values stronger conjectures

Cite

@article{arxiv.1003.1646,
  title  = {On stronger conjectures that imply the Erd\"os-Moser conjecture},
  author = {Bernd C. Kellner},
  journal= {arXiv preprint arXiv:1003.1646},
  year   = {2012}
}

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7 pages

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