A DIRECT SOLUTION OF THE QUADRATIC CONGRUENCE x2 ≡ ±p(mód pq) WITH p AND q PRIMES.
Keywords:
QUADRATIC CONGRUENCES, COMPOSITE MODULE, THEORY OF NUMBERSAbstract
In this investigation, a simple procedure is proposed to determine the solutions of the quadratic congruence of composite modulus x2 ≡±p(mod pq), donde p y q are different primes. In the case that q ≡ 3(mód 4) an explicit formula is given for the solutions of the congruence. In addition, an illustration of the procedure is presented through of examples
References
Arrufat González, J. M. (2012). Implementación eficiente del Teorema Chino del Resto. Almería: Máster en informática insdustrial posgrado en informática. Obtenido de http://repositorio.ual.es/bitstream/handle/10835/1869/Trabajo_7036_92.pdf;jsessionid=D49213292618CF44CE1D8F0A08832C6C?sequence=1
Hensel, K. W. (1897). Über eine neue Begründung der Theorie der algebraischen Zahlen. Deutschen Mathematiker-Vereinigung, 84-87. Obtenido de http://www.digizeitschriften.de/dms/img/?PID=PPN37721857X_0006|log2&physid=phys2#navi
Koshy, T. (2007). Elementary Number Theory whith Applications (Segunda ed.). Academic Press is an imprint of Elsevier.
Maheswari, A., & Durairaj, P. (2017). An Algorithm to Find Square Roots of Quadratic Residues Modulo p (p being an odd prime) p≡ 1(mod 4). Global Journal of Pure and Applied Mathematics, XIII(4), 1223-1239. Obtenido de https://www.ripublication.com/gjpam17/gjpamv13n4_09.pdf
Nieto Said, J. H. (2014). Teoría de Números para Olimpiadas de Matemáticas. Caracas, Venezuela: Asociación Venezolana de Competencias Matemáticas. Obtenido de https://acmfiles.s3.amazonaws.com/Libros/TNumerosOlimpiadas.pdf
Piazza, N. (29 de March de 2018). The Chinese Remainder Theorem. Sacred Heart University. Obtenido de https://digitalcommons.sacredheart.edu/cgi/viewcontent.cgi?article=1217&context=acadfest#:~:text=The%20Chinese%20Remainder%20Theorem%20is,pairwise%20rel%2D%20atively%20prime%20moduli.
Pocklington, H. C. (Febrary de 1917). The Direct Solution of the Quadratic and Cubic Binomial Congruences with prime moduli. Proceedings of the Cambridge Philosophical Society, 19, 57-58. Obtenido de https://ia800301.us.archive.org/25/items/proceedingsofcam1920191721camb/proceedingsofcam1920191721camb_bw.pdf
Roy, B. (2018). Formulation of solutions of some classes of standard quadratic congruence of compositive modulus as a produc of a prime-power integer & two or four. International Journal for Research Trends and Innovarion, 3, 120-122. Obtenido de https://ijrti.org/papers/IJRTI1805023.pdf
Roy, B. (2018). Formulation of solutions of standard quadratic congruence of even compositive modulus. International Journal of Research Science & Management, 99-101. Obtenido de http://www.ijrsm.com/issues%20pdf%20file/Archive-2018/May-2018/13.pdf
Rubiano, G. N., Gordillo, J. E., & Jiménez, L. R. (2004). Teoría de Números (para principiantes) (Segunda ed.). Bogotá, Colombia: Universidad Nacional de Colombia. Obtenido de https://matcris5.files.wordpress.com/2011/08/teoria_de_los_numeros_para_principiantes1.pdf
Wright, S. (Noviembre de 2016). Introducción: Resolviendo la Congruencia Cuadrática General Módulo a Primo. Obtenido de Researchgate: https://www.researchgate.net/publication/310537551_Introduction_Solving_the_General_Quadratic_Congruence_Modulo_a_Prime
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