Let A be the set of all polynomials f with positive integral coefficients such that $f(n)|(2^n-1)$ for all $A\in\mathbb{N}$. Then $$\sum_{f\in A} {1\over f(2019)}=?$$
I tried to define a polynomial, but where is the degree? Hence I considered all polynomials that leave remainder $1$ mod $f.$ Hence $2^n-1$ is divisible. But actually I cannot guess how to proceed! Please help!