# From strict to non-strict

Algebra Level 4

Let $$a$$ and $$b$$ be positive integers such that $$\frac{ab}{a + b} > 2017.$$ Let $$C$$ be the greatest possible real number such that $$\frac{ab}{a + b} \geq C.$$ If $$C$$ can be written in the form $$\frac{p}{q},$$ where $$p$$ and $$q$$ are coprime positive integers, find the last three digits of $$q.$$

×