Characterization of Chebyshev Numbers

• Date: 2018
• Main Authors: Jacobs, David Pokrass, Rayes, Mohamed O., Trevisan, Vilmar
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: Chebyshev polynomials; polynomial factorization; resultant; pseudoprimes; Carmichael numbers; 11A07; 11Y35
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/809
• Journal Title: 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...