Characterization of Chebyshev Numbers

• Datum: 2018
• Hauptverfasser: Jacobs, David Pokrass, Rayes, Mohamed O., Trevisan, Vilmar
• Format: Artikel
• Sprache: English
• Veröffentlicht: Lugansk National Taras Shevchenko University 2018
• Schlagworte: Chebyshev polynomials; polynomial factorization; resultant; pseudoprimes; Carmichael numbers; 11A07; 11Y35
• Online Zugang: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/809
• Назва журналу: Algebra and Discrete Mathematics

Let \(T_n(x)\) be the degree-\(n\) Chebyshev polynomial of the first kind. It is known [1,13] that \(T_p(x) \equiv x^p \bmod{p}\), when \(p\) is an odd prime, and therefore, \(T_p(a) \equiv a \bmod{p}\) for all \(a\). Our main result is the characterization of composite numbers \(n\) satisfying the...