abstract algebra - Modular Arithmetic - Are we allowed to distribute the Modularity?

Assume I have a problem such as "Prove that $\displaystyle103^{53} + 53^{103}$ is divisible by $39$."
This would mean I wanted to prove that $\displaystyle103^{53} + 53^{103}\equiv0\pmod{39}$.

My starting statement would be then "$\displaystyle103^{53} + 53^{103}\pmod{39}$" and I would then equate this to "$\displaystyle103^{53}\pmod{39} + 53^{103}\pmod{39}$" and then continue.

Am I allowed to distribute the mod like that?

Thanks.