On stronger conjectures that imply the Erdös-Moser conjecture

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 $k\ge 2$. We show that stronger conjectures about consecutive values of the function $S_k$, that seem to be more naturally, imply the Erdös-Moser conjecture.

7 pages

References in corpus (2)

• On irregular prime power divisors of the Bernoulli numbers
• The Erdős--Moser equation $1^k+2^k+...+(m-1{)}^k=m^k$ revisited using continued fractions

Cited by in corpus (3)

• The $p$-adic Order of Power Sums, the Erdös-Moser Equation, and Bernoulli Numbers
• Forbidden integer ratios of consecutive power sums
• Integer ratios of consecutive alternating power sums