TY - JOUR ID - 81593 TI - An Alternative Proof for a Theorem of R.L. Graham Concerning CHEBYSHEV Polynomials JO - Journal of Algorithms and Computation JA - JAC LA - en SN - 2476-2776 AU - Ramasamy, A.M.S.. AU - Ponraj, R AD - Department of Mathematics, Pondicherry University, Pondicherry, India AD - Department of Mathematics Sri Parakalyani College Alwarkurichi -627 412, India Y1 - 2021 PY - 2021 VL - 53 IS - 1 SP - 117 EP - 122 KW - Chebyshev polynomials KW - Pell's equation KW - prime factorization DO - 10.22059/jac.2021.81593 N2 - 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 $D \in N$. UR - https://jac.ut.ac.ir/article_81593.html L1 - https://jac.ut.ac.ir/article_81593_93d781a6ea7bffe6615c83f4372cea32.pdf ER -