On stronger conjectures that imply the Erdös-Moser conjecture

Details On stronger conjectures that imply the Erdös-Moser conjecture On stronger conjectures that imply the Erdös-Moser conjecture

2010-03-08

arxiv.org/abs/1003.1646v1

Mathematics

Number Theory

9 pages

Scientific paper

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.

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