Geodesic
Integer triangles, Pell's equation and Chebyshev polynomials
Vestnik rossijskih universitetov. Matematika, Tome 24 (2019) no. 126, pp. 179-186

Voir la notice de l'article provenant de la source Math-Net.Ru

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, Chebyshev polynomials.
Mots-clés : Heron’s formula, Pell’s equation 
V. F. Molchanov; E. S. Yuryeva. Integer triangles, Pell's equation and Chebyshev polynomials. Vestnik rossijskih universitetov. Matematika, Tome 24 (2019) no. 126, pp. 179-186. http://geodesic.mathdoc.fr/item/VTAMU_2019_24_126_a3/
@article{VTAMU_2019_24_126_a3,
     author = {V. F. Molchanov and E. S. Yuryeva},
     title = {Integer triangles, {Pell's} equation and {Chebyshev} polynomials},
     journal = {Vestnik rossijskih universitetov. Matematika},
     pages = {179--186},
     year = {2019},
     volume = {24},
     number = {126},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTAMU_2019_24_126_a3/}
}
TY  - JOUR
AU  - V. F. Molchanov
AU  - E. S. Yuryeva
TI  - Integer triangles, Pell's equation and Chebyshev polynomials
JO  - Vestnik rossijskih universitetov. Matematika
PY  - 2019
SP  - 179
EP  - 186
VL  - 24
IS  - 126
UR  - http://geodesic.mathdoc.fr/item/VTAMU_2019_24_126_a3/
LA  - ru
ID  - VTAMU_2019_24_126_a3
ER  - 
%0 Journal Article
%A V. F. Molchanov
%A E. S. Yuryeva
%T Integer triangles, Pell's equation and Chebyshev polynomials
%J Vestnik rossijskih universitetov. Matematika
%D 2019
%P 179-186
%V 24
%N 126
%U http://geodesic.mathdoc.fr/item/VTAMU_2019_24_126_a3/
%G ru
%F VTAMU_2019_24_126_a3

[1] I. V. Arnold, Number Theory, Uchpedgiz, Moscow, 1939 (In Russian)

[2] A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher Transcendental Functions, v. 2, Bateman Manuscript Project, McGraw-Hill, New York, 1953 | MR

[3] N. Ya. Vlenkin, Combinatorial Analysis, Nauka, Moscow, 1969 (In Russian) | MR

[4] A. O. Gelfond, Calculus of Finite Differences, Gostekhizdat, M–L., 1952 (In Russian) | MR

[5] A. Yu. Evnin, “Pell's equations”, Mathematics in Higher Education, 7 (2013), 89–94 (In Russian)