Determine all positive integers $n$ which have a divisor $d$ with the property that $dn + 1$ is a divisor of $d^2 + n^2$.
Problem
Source: New Zealand NZMOC Camp Selection Problems 2015 p8
Tags: divides, divisible, divisor, number theory
Source: New Zealand NZMOC Camp Selection Problems 2015 p8
Tags: divides, divisible, divisor, number theory
Determine all positive integers $n$ which have a divisor $d$ with the property that $dn + 1$ is a divisor of $d^2 + n^2$.