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Russian Universities Reports. Mathematics, 2019, Volume 24, Issue 126, Pages 179–186
DOI: https://doi.org/10.20310/1810-0198-2019-24-126-179-186 (Mi vtamu145) 		 
Scientific articles

Integer triangles, Pell's equation and Chebyshev polynomials

V. F. Molchanov, E. S. Yuryeva

Derzhavin Tambov State University
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DOI: https://doi.org/10.20310/1810-0198-2019-24-126-179-186
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.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 3.8515.2017/8.9
The work is supported by the program of the Ministry of Education and Science of the Russian Federation (project no. 3.8515.2017/8.9).
Received: 30.01.2019
Bibliographic databases:
Document Type: Article
UDC: 511.5
Language: Russian
Citation: V. F. Molchanov, E. S. Yuryeva, “Integer triangles, Pell's equation and Chebyshev polynomials”, Russian Universities Reports. Mathematics, 24:126 (2019), 179–186
Citation in format AMSBIB
\Bibitem{MolYur19}
\by V.~F.~Molchanov, E.~S.~Yuryeva
\paper Integer triangles, Pell's equation and Chebyshev polynomials
\jour Russian Universities Reports. Mathematics
\yr 2019
\vol 24
\issue 126
\pages 179--186
\mathnet{http://mi.mathnet.ru/vtamu145}
\crossref{https://doi.org/10.20310/1810-0198-2019-24-126-179-186}
\elib{https://elibrary.ru/item.asp?id=38253922}
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