In terms of $p$ and $k$, compute the number of solutions in positive integers to the equation $ab+bc+ca=p^{2k}$ satisfying $a\leq b\leq c$ where $p$ is a fixed prime and $k$ is a fixed positive integer. Proposed by Alexander Wang
Source: 2022 Revenge ELSMO #1
Tags: algebra, revenge elmo, revenge elsmo, relmo
In terms of $p$ and $k$, compute the number of solutions in positive integers to the equation $ab+bc+ca=p^{2k}$ satisfying $a\leq b\leq c$ where $p$ is a fixed prime and $k$ is a fixed positive integer. Proposed by Alexander Wang