From: alainverghote on
Good day sunshine...

Building duos of squares seems easy .
Since any integer factorizable into two distinct factors
of same parity is equal to one (at least) difference of two squares:
Ex: 105=5*21 = 7*15 = 1*105 ,we begin with two known values
4^2 + ... = 11^2+...
4^2 + 5*21 = 11^2
4^2 + (13-8)(13+8) = 11^2
4^2 + 13^2 = 11^2+8^2
............
4^2+53^2 = 11^2 + 52^2

This process was used in many squares Catalan equalities,

Alain