MathDB
F 4

Source:

May 25, 2007
trigonometryquadraticsrational numbers

Problem Statement

Suppose that tan⁡α=pq\tan \alpha =\frac{p}{q}, where pp and qq are integers and q≠0q \neq 0. Prove the number tan⁡β\tan \beta for which tan⁡2β=tan⁡3α\tan 2\beta =\tan 3\alpha is rational only when p2+q2p^2 +q^2 is the square of an integer.
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