Reformulation of a Special Standard Quadratic Congruence of Even Composite Modulus

Prof. B. M. Roy

Composite Modulus; Quadratic Congruence; Reformulations

A very special type of standard quadratic congruence of even composite modulus is reformulated in this paper. The formulation found in the literature of mathematics is not sufficient. The formulation found is only for an odd positive integer but nothing is said about even positive integer. So, an incomplete formulation is found in the literature. The author has taken the opportunity to find a complete formulation of the said quadratic congruence of even composite modulus and has presented a complete formulation of the congruence.

[1] Roy B M, “Discrete Mathematics & Number Theory”, 1/e, ISBN: 978-93-84336-12-7, Jan. 2016,Das GanuPrakashan, Nagpur, page-88. [2] Niven I., Zuckerman H. S., Montgomery H. L. (1960, Reprint 2008), “An Introduction to The Theory of Numbers”, 5/e, Wiley India (Pvt) Ltd, page-148, problem-11. [3] Roy B M, 2018, A new method of finding solutions of a solvable standard quadratic congruence of comparatively large prime modulus, International Journal of Advanced Research, Ideas and Innovations in Technology (IJARIIT), ISSN: 2454-132X, Vol-4, Issue-3, May-Jun-18. [4] Roy B M, 2018, Formulation of solutions of standard quadratic congruence of even composite modulus as a product of two odd primes & four, International Journal of Recent Innovations In Academic Research (IJRIAR), ISSN:2635-3040, Vol-2, Issue-2, Jun-18. [5] Roy B M, 2018, Formulation of solutions of standard quadratic congruence of even composite modulus as a product of two odd primes & eight, International Journal of Advanced Research, Ideas and Innovations in Technology (IJARIIT), ISSN: 2454-132X, Vol-4, Issue-4, July-18. [6] Roy B M, 2018, Formulation of solutions of some classes of standard quadratic congruence of composite modulus as a product of a prime-power integer by two or four, International Journal for Research Trends and Innovations(IJRTI), ISSN:2456-3315, Vol-3, Issue-5, May-18. [7] Roy B M, 2018, Formulation of Standard Quadratic Congruence of Composite modulus as a product of prime-power integer and eight, International Journal of Science & Engineering Development Research (IJSDR),ISSN: 2455-2631, Vol-3, Issue-7, Jul-18. [8] Roy B M, 2018, Formulation of solutions of a class of standard quadratic congruence of even composite modulus, International Journal of Science & Engineering Development Research (IJSDR), ISSN: 2455-2631, Vol-3, Issue-8, Jul-18. [9] Roy B M, 2018, An Algorithmic Formulation of solving Standard Quadratic Congruence of Prime- power Modulus, International Journal of Advanced Research, Ideas and Innovations in Technology (IJARIIT), ISSN: 2454-132X, Vol-4, Issue-6, Dec-18. [10] Roy B M, 2019, Formulation of a Class of Solvable Standard Quadratic Congruence of Even Composite Modulus, International Journal for Research Trends and Innovations (IJRTI), ISSN: 2456-3315, Vol-4, Issue-3, Mar-19. [11] Roy B M, 2019, Formulation of Some Classes of Solvable Standard Quadratic Congruence modulo a Prime Integer – Multiple of Three & Ten, International Journal of Scientific Research and Engineering Development ( IJSRED), ISSN: 2581-7175, Vol-2, Issue-2, Mar-19.