Problem

Source: Austrian Mathematics Olympiad Regional Competition (Qualifying Round) 2017, Problem 4

Tags: number theory, Sum of Squares, Divisors, Divisibility



Determine all integers $n \geq 2$, satisfying $$n=a^2+b^2,$$where $a$ is the smallest divisor of $n$ different from $1$ and $b$ is an arbitrary divisor of $n$. Proposed by Walther Janous