IMO 1985 LL FRA24

Let d \geq1 be an integer that is not the square of an integer.

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IMO 1985 LL FRA24

Origin: FRA

Problem

Let d \geq1 be an integer that is not the square of an integer. Prove that for every integer n \geq1, (n \sqrt d + 1)| sin(n\pi \sqrt d)| \geq1.