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How many real xxx satisfying 0≤x≤20170 \leq x \leq 20170≤x≤2017 are there such that xsin(πx)x \sin(\pi x)xsin(πx) is an integer?
Bonus: Can you come up with a simple formula for how many 0≤x≤n0 \leq x \leq n0≤x≤n there are such that xsin(πx)x \sin(\pi x) xsin(πx) is an integer, where nnn is a positive integer?
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