Question 17
Let $f:\mathbb{R}\to\mathbb{R}$ be defined by
$$f(x)=x+2x^2+3x^3+\cdots+100x^{100}.$$
Find the number of positive integers $x\ne1$ for which the integer $f(x)$ is divisible by the integer $x-1$.
$$f(x)=x+2x^2+3x^3+\cdots+100x^{100}.$$
Find the number of positive integers $x\ne1$ for which the integer $f(x)$ is divisible by the integer $x-1$.