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Trigonometric equation

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September 1, 2010
trigonometrynumber theoryrelatively primealgebraequationIMO ShortlistIMO Longlist

Problem Statement

Show that the numbers tan⁡(rπ15)\tan \left(\frac{r \pi }{15}\right), where rr is a positive integer less than 1515 and relatively prime to 1515, satisfy x8−92x6+134x4−28x2+1=0.x^8 - 92x^6 + 134x^4 - 28x^2 + 1 = 0.
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