Determine all positive integers $a$, $b$ and $c$ which satisfy the equation $$a^2+b^2+1=c!.$$ Proposed by Nikola Velov
Problem
Source: 2022 Junior Macedonian Mathematical Olympiad P1
Tags: number theory, Diophantine equation, factorial
Source: 2022 Junior Macedonian Mathematical Olympiad P1
Tags: number theory, Diophantine equation, factorial
Determine all positive integers $a$, $b$ and $c$ which satisfy the equation $$a^2+b^2+1=c!.$$ Proposed by Nikola Velov