University of TehranJournal of Algorithms and Computation2476-277653120210601An Alternative Proof for a Theorem of R.L. Graham Concerning CHEBYSHEV Polynomials11712281593ENA.M.S..RamasamyDepartment of Mathematics, Pondicherry University, Pondicherry, IndiaRPonrajDepartment of Mathematics
Sri Parakalyani College
Alwarkurichi -627 412, IndiaJournal Article20210529In 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 $D in N$.https://jac.ut.ac.ir/article_81593_93d781a6ea7bffe6615c83f4372cea32.pdf