Hi all. A friend asked me an interesting question about representations of integers as sums of two squares: what could be a condition, given , for n to have two different representations (ie. two different couples such that ) as a sum of two squares? I was wondering if someone could help!

I haven't much knowledge (yet) in number theory or fields/rings (but I did study some about groups), but feel free to use any definitions and I'll just look them up. Any direction would also be nice (instead of a solution).

Happy new year, and again thanks for any help.