MathDB

1

Part of 1985 Iran MO (2nd round)

Problems(2)

The number is an integer (Cosine) - [Iran Second Round 1985]

Source:

12/28/2010
Let α\alpha be an angle such that cos⁡α=pq\cos \alpha = \frac pq, where pp and qq are two integers. Prove that the number qncos⁡nαq^n \cos n \alpha is an integer.
trigonometryinductionstrong inductionalgebra proposedalgebra
Inscribe a triangle - [Iran Second Round 1985]

Source:

12/29/2010
Inscribe in the triangle ABCABC a triangle with minimum perimeter.
geometrycircumcircleinequalitiesgeometry proposed