Let $\Phi_m(x)$ and $\Phi_n(x)$ be two different cyclotomic polynomials. Then $\Phi_m(x)$ and $\Phi_n(x)$ are coprime, so there are two polynomials $s(x), t(x)$ with, say, rational coefficients such that $s(x)\Phi_m(x)+t(x)\Phi_n(x)=1$.
Question. Can one find these $s$ and $t$ with integer coefficients?
I think the answer is "yes".