Formula for Number of Fixed Points of Digraph Arising from The Relation a^6 ≡ b (mod n) And Some Generalization
Main Article Content
Abstract
For an integer such that , this article provides a formula for number of fixed points of the digraph which has the vertex set and directed edges if and only if by using the knowledge about the factorization of the cyclotomic polynomial and extend the result to formula for number of fixed points of digraph where is an integer such that and is a prime number.
Article Details
References
รตินันท์ บุญเคลือบ และ ธัญพิชชา ยอดแก้ว. (2561). ไดกราฟที่เกิดจากความสัมพันธ์ a^4 ≡ b (mod n). วารสารคณิตศาสตร์ โดยสมาคมคณิตศาสตร์แห่งประเทศไทย ในพระบรมราชูปถัมภ์, 63 (695), น. 9 - 18.
Boonklurb, R. and Yodkeaw, T. (2018). Digraph Arising from The Relation a^4 ≡ b (mod n). Mathematical Journal by The Mathematical Association of Thailand under The Patronage of His Majesty the King, 63 (695), p. 9 - 18.
อัจฉรา หาญชูวงศ์. (2542). ทฤษฎีจำนวน. กรุงเทพมหานคร: โรงพิมพ์แห่งจุฬาลงกรณ์มหาวิทยาลัย.
Harnchoowong, A. (1999). Theory of Numbers. Bangkok: Chulalongkorn Unversity Printery.
Ju, T. and Wu, M. (2014). On Iteration Digraph and Zero-Divisor Graph of Ring Z_n. Czechoslovak Mathematical Journal, 64 (139), p. 611 - 628.
Kanoksing, P. (2017). Structure of the quotient ring of polynomials over integer modulo m with the nth cyclotomic polynomial. (Senior Project). Chulalongkorn University, Faculty of Science, Department of Mathematics and Computer Science.
Meemark, Y. (2016). Theory of Numbers. Retrieved from http://pioneer.netserv.chula.ac.th/~myotsana/MATH331NT.pdf.
Rosen, K. H. (1999). Discrete Mathematics and Its Applications (4th ed.). McGraw-Hill International Edition.
Skowronex-KaziÓw, J. (2009). Properties of Digraphs Connected with Some Congruence Relations. Czechoslovak Mathematical Journal, 59 (134), p. 39 - 49.
Somer, L. and Křížek, M. (2011). The Structure of Digraphs Associated with the Congruence x^k ≡ y (mod n). Czechoslovak Mathematical Journal, 61 (136), p. 337 - 358.
Szalay, L. (1992). A discrete iteration in number theory. BDTF Tud. Közl., 8, p. 71 - 91 (in Hungarian).