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An Alternative Proof for a Theorem of R.L. Graham Concerning CHEBYSHEV Polynomials | ||
| Journal of Algorithms and Computation | ||
| دوره 53، شماره 1، شهریور 2021، صفحه 117-122 اصل مقاله (240.97 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22059/jac.2021.81593 | ||
| نویسندگان | ||
| A.M.S.. Ramasamy* 1؛ R Ponraj2 | ||
| 1Department of Mathematics, Pondicherry University, Pondicherry, India | ||
| 2Department of Mathematics Sri Parakalyani College Alwarkurichi -627 412, India | ||
| چکیده | ||
| 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 $D \in N$. | ||
| کلیدواژه‌ها | ||
| Chebyshev polynomials؛ Pell's equation؛ prime factorization | ||
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آمار تعداد مشاهده مقاله: 278 تعداد دریافت فایل اصل مقاله: 199 |
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