Find the remainder Of an equation

Question

Let, $S = 1^1 + 2^2 + 3^3 + 4^4 + \ldots + 2016^{2016}$. What is the remainder when $S$ is divided by $2$?

Please give us an explanations for newbies like us.

Answer 1

Every second term is even so has remainder 0 when divided by 2. Every other term is odd, so has remainder 1 when divided by 2. The result is then $$\frac{2016}{2}=1008=0 \mod{2}$$ I.e. the remainder is 0 when divided by 2.