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Inequality with sine

Source:

September 13, 2010
inequalitiestrigonometryinequalities unsolvedalgebra

Problem Statement

Let d≥1d \geq 1 be an integer that is not the square of an integer. Prove that for every integer n≥1,n \geq 1, (nd+1)⋅∣sin⁡(nπd)∣≥1(n \sqrt d +1) \cdot | \sin(n \pi \sqrt d )| \geq 1
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