what is remainder when in the following scenario? What is the remainder when $x^{2016} - 1$ is divided by 
$ x^{5}+x^{4}+x^{3}+x^{2}+x+1 ?$
how to solve this kind of problem.

$$x^{2016}-1=(x-1)(x^{2015}+x^{2014}+\cdots+x+1)$$
When you divide $x^{2015}+x^{2014}+\cdots+x+1$ by $x^5+x^4+x^3+x^2+x+1$ by long division, $6$ terms cancel out from the dividend at each step. For example, in the first step, the quotient term is $x^{2010}$, which on multiplication with $x^5$ cancels out $x^{2015}$, $x^4$ cancels out $x^{2014}$, and so on till $x^{2010}$. After this, the process repeats starting with $x^{2009}$. In all, the dividend has $2016$ terms, which is divisible by $6$. Hence, $x^{2015}+x^{2014}+\cdots+x+1$ is divisible by $x^5+x^4+x^3+x^2+x+1$, and as a result, $x^{2016}-1$ is also divisible by it.
Thus, the remainder is $0$.
