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.

The principle is that if $a\equiv a'\pmod n$ and $b\equiv b'\pmod n$, then $ab\equiv a'b'\pmod n$; and similarly for addition instead of multiplication.
