What is the smallest integer that can be presented as a sum of 2 squares of distinct integers in 7 different ways?
I started looking into how to solve this problem and found this site which explains how to find integers which can be expressed as a sum of two squares in N ways:
https://www.primepuzzles.net/puzzles/puzz_062.htm
They go a lot further than the N=7 that is in our problem statement.