2 problems

Let $f(x_1,\ldots,x_k)$ be a multivariable polynomial with integral coefficients. Write $Z_m^*=\{x\in\mathbb N\mid \gcd(x,m)=1,\ x\leq m\}$. Assume that there is a positive integer…

Let $f(x)$ be an irreducible polynomial with integral coefficients and positive leading coefficient. Assume that there is no integer $d>1$ dividing $f(k)$ for every integer $k$. Le…