An Analytical Exploration of the Erdös-Moser Equation ${\sum }_{i=1}^{m-1}{i}^k=m^k$ Using Approximation Methods

Guillaume Lambard

The Erdös-Moser equation ${\sum }_{i=1}^{m-1}{i}^k=m^k$ is a longstanding challenge in number theory, with the only known integer solution being $(k,m)=(1,3)$. Here, we inve…