PORTUGALIAE MATHEMATICA Vol. 52, No. 3, pp. 301304 (1995) 

A Problem of DiophantosFermat and Chebyshev Polynomials of the Second KindGheorghe UdreaStr. Unirii  Siret, Bl. 7A, SC. I., AP. 17,TârguJiu, 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. Full text of the article:
Electronic version published on: 29 Mar 2001. This page was last modified: 27 Nov 2007.
© 1995 Sociedade Portuguesa de Matemática
