100 Degree FunctionNumber 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.