# 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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