# Isn't it just 413?

**Number Theory**Level 5

\(f(x)\) is a polynomial of degree \(413\) with non-negative integral coefficients such that \(f(1)=612^{1025}.\) John is a genie that will tell you \(f(x)\) for any \(x\) you tell him. What is the minimum number of \(\textit{additional}\) values of \(f(x)\) you must ask John for to be able to uniquely determine the polynomial?