Given a certain integer $n$ and a certain sequence of integers $a_0, a_1, a_2, ..., a_n$, for any positive integer x, if $f(x)=a_0+a_1x^1+a_2x^2+...+a_{n-1}x^{n-1}+a_nx^n$ is a multiple of a certain positive integer k, then Let's say K is a set of k.
I want to know how to find the largest integer among K.
For example, when $f(x)=4x+4$ (it's meaning that $a_0=4, a_1=4, n=1$) then, $f(1)=8, f(2)=12, f(3)=16...$ and K={1, 2, 4} Since 4 is the largest, the answer I want is 4.
I think that when n=1, Bézout's Identity can be used to prove that the maximum value of K is $gcd(a_0, a_1)$, but I'm not sure. help.
