Целочисленные треугольники, уравнение Пелля и многочлены Чебышева

Abstract

In this paper we consider some types of integer triangles: “almost equilateral”, rectangular “almost isosceles”, rectangular “whose angle is almost 300”. 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.