The Erdős--Moser equation $1^k+2^k+...+(m-1{)}^k=m^k$ revisited using continued fractions

Yves Gallot, Pieter Moree, Wadim Zudilin

If the equation of the title has an integer solution with $k\ge 2$, then $m>10^{9.3\cdot 10^6}$. This was the current best result and proved using a method due to L. Moser (1953). Th…