Consider a function $f(x) = x^4+x^3+x^2+x+1$, where x is an integer, $x\gt 1$. What will be the remainder when $f(x^5)$ is divided by $f(x)$? Consider a function $f(x) = x^4+x^3+x^2+x+1$, where x is an integer, $x\gt 1$. What will be the remainder when $f(x^5)$ is divided by $f(x)$ ?
$f(x)=x^4+x^3+x^2+x+1$
$f(x^5)=x^{20}+x^{15}+x^{10}+x^5+1$

$f_1(x)=x+1$
$f_1(x^5)=x^5+1$
$f_1(x^5)$, when divided by $f_1(x)$ leaves a remainder 0.
$f_2(x)=x^2+x+1$
$f_2(x^5)=x^{10}+x^5+1$
$f_2(x^5)$, when divided by $f_2(x)$ leaves a remainder 0.
