PORTUGALIAE MATHEMATICA Vol. 52, No. 3, pp. 363378 (1995) 

Note on the Chebyshev Polynomials and Applications to the Fibonacci NumbersJosé MorgadoCentro de Matemática da Faculdade de Ciências da Universidade do Porto,Porto  PORTUGAL Abstract: In [12], Gheorghe Udrea generalizes a result obtained in [8], by showing 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 $$ \Bigl\{U_{n},\,U_{n+2r},\,U_{n+4r},\,4U_{n+r}U_{n+2r}U_{n+3r}\Bigr\}, r,n\in\N, $$ increased by $U_{a}^{2}U_{b}^{2}$, for suitable nonnegative 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
