Finding the remainder when $2^{100}+3^{100}+4^{100}+5^{100}$ is divided by $7$ 
Find the remainder when $2^{100}+3^{100}+4^{100}+5^{100}$ is divided by $7$.

Please brief about the concept behind this to solve such problems. Thanks.

Fermat's little theorem says that $a^6\equiv 1 \pmod 7$ whenever $7$ does not divide $a$.  So $2^{100}+3^{100}+4^{100}+5^{100}\equiv 2^4+3^4+4^4+5^4 \pmod 7$
