Solution of the Erdös-Moser Equation 1+2^p+3^p+⋯〖+k〗^p=(k+1)^p

Abstract

The Erdos-Moser equation (EM equation), named after Paul Erdos and Leo Moser, has been studied by many number theorists throughout history since combines addition, powers and summation together. An open and very interesting conjecture of Erdos-Moser states that there is no other solution of the EM equation than trivial 1+2=3. Investigation of the properties and identities of the EM equation and ultimately prove the conjecture is the main purpose of this article.