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dc.contributor.author Jacobs, D.P.
dc.contributor.author Trevisan, V.
dc.contributor.author Rayers, M.O.
dc.date.accessioned 2019-06-10T19:03:32Z
dc.date.available 2019-06-10T19:03:32Z
dc.date.issued 2008
dc.identifier.citation Characterization of Chebyshev Numbers / D.P. Jacobs, V. Trevisan, M.O. Rayers // Algebra and Discrete Mathematics. — 2008. — Vol. 7, № 2. — С. 65–82. — Бібліогр.: 17 назв. — англ. uk_UA
dc.identifier.issn 1726-3255
dc.identifier.other 2000 Mathematics Subject Classification:11A07, 11Y35.
dc.identifier.uri http://dspace.nbuv.gov.ua/handle/123456789/152391
dc.description.abstract Let Tn(x) be the degree-n Chebyshev polynomial of the first kind. It is known [1,13] that Tp(x)≡xpmodp, when p is an odd prime, and therefore, Tp(a)≡amodp for all a. Our main result is the characterization of composite numbers n satisfying the condition Tn(a)≡amodn, for any integer a. We call these pseudoprimes Chebyshev numbers, and show that n is a Chebyshev number if and only if n is odd, squarefree, and for each of its prime divisors p, n≡±1modp−1 and n≡±1modp+1. Like Carmichael numbers, they must be the product of at least three primes. Our computations show there is one Chebyshev number less than 10¹⁰, although it is reasonable to expect there are infinitely many. Our proofs are based on factorization and resultant properties of Chebyshev polynomials. uk_UA
dc.description.sponsorship Research partially supported by CNPq - Grants 478290/04-7 and 43991/2005-0;and FAPERGS - Grant 05/2024.1 uk_UA
dc.language.iso en uk_UA
dc.publisher Інститут прикладної математики і механіки НАН України uk_UA
dc.relation.ispartof Algebra and Discrete Mathematics
dc.title Characterization of Chebyshev Numbers uk_UA
dc.type Article uk_UA
dc.status published earlier uk_UA

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