2016 is absolutely awesome 19

Algebra Level 5

Let \(f(x) = x^2 − ax + b\), where \(a\) and \(b\) are positive integers.

How many pairs of positive integers \((a, b)\) with \(1\le a, b\le 2016\) for which every root of \(f(f(x)) − x\) is an integer?


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