Counting Conundrum

Geometry Level 3

How many real \(x\) satisfying \(0 \leq x \leq 2017\) are there such that \(x \sin(\pi x)\) is an integer?

Bonus: Can you come up with a simple formula for how many \(0 \leq x \leq n\) there are such that \(x \sin(\pi x) \) is an integer, where \(n\) is a positive integer?