Find the remainder when $x^{100}$ is divided by $x^8 - x^6 + x^4 - x^2 + 1.$ I need help in the problem:
Find the remainder when $x^{100}$ is divided by $x^8 - x^6 + x^4 - x^2 + 1.$
I have tried factoring $x^{100}-1$ and adding 1 to that, but that hasn't helped. Could someone please help with this?

Hint
Replace $x^2$ with to find the divisor $$=\dfrac{y^5+1}{y+1}$$
$y^{50}=(y^5+1-1)^{10}=1+$ terms divisible by $y^5+1$
