Scientific articles

Integer triangles, Pell's equation and Chebyshev polynomials

V. F. Molchanov, E. S. Yuryeva

Derzhavin Tambov State University

Abstract: In this paper we consider some types of integer triangles: “almost equilateral”, rectangular “almost isosceles”, rectangular "whose angle is almost $30^\circ$". The description is reduced to Pell's equation. We state the theory of Pell's equation on the basis of an “iterated matrix”. Powers of this matrix are expressed in terms of Chebyshev polynomials.

Keywords: integer triangles, Heron’s formula, Pell’s equation, Chebyshev polynomials.

UDC: 511.5

Received: 30.01.2019

DOI: 10.20310/1810-0198-2019-24-126-179-186

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