Portugaliæ Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 52, No. 3, pp. 301-304 (1995)

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A Problem of Diophantos-Fermat and Chebyshev Polynomials of the Second Kind

Gheorghe Udrea

Str. Unirii - Siret, Bl. 7A, SC. I., AP. 17,
Târgu-Jiu, Codul 1400, Judetul Gorj - ROMÂNIA

Abstract: One shows that, if $(U_{n})_{n\ge0}$ is the sequence of Chebyshev polynomials of the second kind, then the product of any two distinct elements of the set $$ \Bigl\{U_{m},U_{m+2r},U_{m+4r};\,4\cdot U_{m+r}\cdot U_{m+3r}\Bigr\}, m,r\in\N, $$ increased by $U_{a}^{2}\cdot U_{b}^{2}$, for suitable positive integers $a$ and $b$, is a perfect square.
This generalizes a result obtained by José Morgado in [4].

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Electronic version published on: 29 Mar 2001. This page was last modified: 27 Nov 2007.

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