Journal of Integer Sequences, Vol. 19 (2016), Article 16.2.8

Minimal Polynomials of Algebraic Cosine Values at Rational Multiples of π


Pinthira Tangsupphathawat
Department of Mathematics
Phranakhon Rajabhat University
Bangkok 10220
Thailand

Vichian Laohakosol
Department of Mathematics
Faculty of Science
Kasetsart University
Bangkok 10900
Thailand

Abstract:

Lehmer proved that the values of the cosine function evaluated at rational multiples of π are algebraic numbers. We show how to determine explicit, closed form expressions for the minimal polynomials of these algebraic numbers.

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Received February 8 2016. Revised version received March 15 2016. Published in Journal of Integer Sequences, March 19 2016.

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