Prove that there don't exist positive integer numbers $k$ and $n$ which satisfy equation $n^n+(n+1)^{n+1}+(n+2)^{n+2} = 2023^k$. Proposed by Mykhailo Shtandenko
Source: Kyiv City MO 2023 7.3
Tags: number theory
Prove that there don't exist positive integer numbers $k$ and $n$ which satisfy equation $n^n+(n+1)^{n+1}+(n+2)^{n+2} = 2023^k$. Proposed by Mykhailo Shtandenko