MathNet 2010 — Part 06 Question 126

Given natural numbers $a$, $b$, $c$, $d$ for which $ab^2 + ad^2 + cb^2 = ba^2 + bd^2 + ca^2$ and the number $a^2 + b^2 + c^2 + d^2$ is prime. Prove that $a = b$.