Calculate $100^{1207} \mod 63$ I try to solve this question: Calculate $100^{1207} \mod 63$. There is the hint that i should calculate $100^{1207} \mod 7$, $100^{1207} \mod 9$, which is easy for me, but I don't see the relationship between this to questions. I guess it must have something to do with the fact, that $7*9 = 63$.

Note that $$100^3\equiv 1 \mod 63$$
