TR-MO-R1 2017 Problem 2

$x, y \geq -2017$ olmak üzere, $\dfrac{x}{x-y+2017} - \dfrac{y}{x-y-2017} = 1$ denklemini sağlayan kaç farklı $(x, y)$ tam sayı ikilileri vardır?

A) $4033$ B) $4034$ C) $6051$ D) $6052$ E) $8068$

Official text Turkish Mathematical Olympiad, first round 2017 official paper, page 3. Quoted with source.

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