Math Help - modulo stuff

1. modulo stuff

Hey all,

I'm trying to find every $k$ for which this is true: $mn \equiv m^2+n^2 (mod_k) \Longleftrightarrow m=n=0$. I'm actually not sure if there are any, and I have no idea how to proceed. Anyone...?

Thank you!!

2. Did you mean m=n=0 or just m==n==0 mod k? If the latter then consider, for example, the difference between k = 7 and k = 11.