Counting Conundrum

Geometry Level 3

How many real xx satisfying 0x20170 \leq x \leq 2017 are there such that xsin(πx)x \sin(\pi x) is an integer?


Bonus: Can you come up with a simple formula for how many 0xn0 \leq x \leq n there are such that xsin(πx)x \sin(\pi x) is an integer, where nn is a positive integer?

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