%0 Journal Article
%T An Alternative Proof for a Theorem of R.L. Graham Concerning CHEBYSHEV Polynomials
%J Journal of Algorithms and Computation
%I University of Tehran
%Z 2476-2776
%A Ramasamy, A.M.S..
%A Ponraj, R
%D 2021
%\ 06/01/2021
%V 53
%N 1
%P 117-122
%! An Alternative Proof for a Theorem of R.L. Graham Concerning CHEBYSHEV Polynomials
%K Chebyshev polynomials
%K Pell's equation
%K prime factorization
%R
%X In this paper, an alternative proof is provided for a theorem of R.L.Graham concerning Chebyshev polynomials. While studying the properties of a double star, R.L.Graham [2] proved a theorem concerning Chebyshev polynomials of the first kind ${T_n (x)}$. The purpose of this paper is to provide an alternative proof for his theorem. Our method is based on the divisibility properties of the natural numbers. One may observe that the Chebyshev polynomials evaluated at integers considered by R.L.Graham match with the solutions of the Pell's equation for a general, square-free $D in N$.
%U https://jac.ut.ac.ir/article_81593_93d781a6ea7bffe6615c83f4372cea32.pdf