Open AccessRP-179: Formulation of Solutions of Standard Bi-Quadratic Congruence Modulo a POSITIVE INTEGER MULTIPLE to nth Power of Four
Author(s) -
B M Roy
Publication year - 2021
Publication title -
international journal for research in applied science and engineering technology
Language(s) - English
Resource type - Journals
ISSN - 2321-9653
DOI - 10.22214/ijraset.2021.36926
Subject(s) - congruence (geometry) , modulo , mathematics , quadratic equation , integer (computer science) , power of two , modulus , pure mathematics , combinatorics , discrete mathematics , arithmetic , computer science , geometry , programming language
In this paper, the author has formulated the solutions of the standard bi-quadratic congruence of an even composite modulus modulo a positive integer multiple to nth power of four. First time a formula is established for the solutions. No literature is available for the current congruence. The author analysed the formulation of solutions in two different cases. In the first case of analysis, the congruence has the formulation which gives exactly eight incongruence solutions while in the second case of the analysis, the congruence has a different formulation of solutions and gives thirty-two incongruent solutions. A very simple and easy formulation to find all the solutions is presented here. Formulation is the merit of the paper.