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A review and reformulation of solutions of the standard quadratic congruence of even composite modulus

Author Affiliations

  • 1Department of Mathematics, Jagat Arts, Commerce & I H P Science College, Goregaon, Dist-Gondia, MS, India

Res. J. Mathematical & Statistical Sci., Volume 10, Issue (1), Pages 9-10, January,12 (2022)

Abstract

A very special type of standard quadratic congruence of composite modulus modulo a power of an even –prime integer is reviewed and found that it was partially formulated for its solutions. The author realised that the earlier formulation is incomplete and a reformulation of the solutions is needed. The author considered the problem for reformulation and reformulated. In the literature of mathematics, an insufficient partial formulation is found in a book of Number Theory. There the formulation is only for an odd positive integer but nothing is said about even positive integer. So, an incomplete formulation is in the literature of mathematics. The author reviewed the problem and provide a complete formulation of the said quadratic congruence and has presented here.

References

  1. Niven I., Zuckerman H. S. and Montgomery H. L. (2008). An Introduction to The Theory of Numbers., 1960, Reprint 2008, 5/e, Wiley India (Pvt) Ltd, problem-11, pp-148,., undefined
  2. Roy B. M. (2016)., Discrete Mathematics & Number Theory., Das Ganu Prakashan, Nagpur, India, ISBN: 978-93-84336-12-7.
  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, 4(3).
  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, 2(2).
  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, 4(4).
  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, 3(5).
  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, 3(7).
  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, 3(8).
  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, 4(6).
  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, 4(3).
  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, 2(2).