# 100 Degree Function

**Number Theory**Level 5

Suppose \(f(x)\) is a polynomial with integer coefficients of degree \(100\). Find the biggest possible number of pairs of integers \(n<m\), such that \(f(n)=m\) and \(f(m)=n\).

**Details and assumptions**

You are asked to find the biggest possible number of pairs, not the biggest pair. Hence, your answer is just an integer, not a pair of integers.