#composite modulus

[ijtsrd]

RP 166 Solving Some Special Standard Cubic Congruence of Composite Modulus modulo a Multiple of an Odd Prime

by Prof B M Roy "RP-166: Solving Some Special Standard Cubic Congruence of Composite Modulus modulo a Multiple of an Odd Prime"

Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-4 , June 2021,

URL: https://www.ijtsrd.compapers/ijtsrd42321.pdf

Paper URL: https://www.ijtsrd.commathemetics/applied-mathamatics/42321/rp166-solving-some-special-standard-cubic-congruence-of-composite-modulus-modulo-a-multiple-of-an-odd-prime/prof-b-m-roy

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Here in this paper, ten special type of standard cubic congruence of composite modulus are studied for their solutions. It is found that each of the cubic congruence under consideration has a single solution. The solution can be obtained orally as the solution is given in the problems. No extra effort is necessary to find the solution. 

[ijtsrd]

RP 163 Solving a Special Standard Quadratic Congruence Modulo an Even Multiple of an Odd Positive Integer

by Prof B M Roy "RP-163: Solving a Special Standard Quadratic Congruence Modulo an Even Multiple of an Odd Positive Integer"

Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-3 , April 2021,

URL: https://www.ijtsrd.com/papers/ijtsrd41116.pdf

Paper URL: https://www.ijtsrd.com/mathemetics/applied-mathematics/41116/rp163-solving-a-special-standard-quadratic-congruence-modulo-an-even-multiple-of-an-odd-positive-integer/prof-b-m-roy

callforpapercommerce, ugcapprovedjournalsincommerce, commercejournal

The author, here in this paper, presented a formulation for solving a special standard quadratic congruence modulo an even multiple of an odd positive integer. The established formula is tested and verified true by solving various numerical examples. The formulation works well and proved time saving. 

[ijtsrd]

RP 165 Solving Some Special Classes of Standard Cubic Congruence of Composite Modulus

by Prof B M Roy "RP-165: Solving Some Special Classes of Standard Cubic Congruence of Composite Modulus"

Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-3 , April 2021,

URL: https://www.ijtsrd.com/papers/ijtsrd39816.pdf

Paper URL: https://www.ijtsrd.com/mathemetics/applied-mathematics/39816/rp165-solving-some-special-classes-of-standard-cubic-congruence-of-composite-modulus/prof-b-m-roy

callforpapersocialscience, ugcapprovedjournalsforsocialscience, socialsciencejournal

In this paper, a special class of standard cubic congruence of composite modulus is studied and formulated the solutions. The discussion is presented here. This cubic congruence has three types of solutions. In first case, it has exactly 3 incongruent solutions in second case, it has nine incongruent solutions and in third case it has twenty seven incongruent solutions. First time a suitable formulation is available for a class of standard cubic congruence. So, formulation is the merit of the paper. 

[ijtsrd]

Formulation of a Class of Standard Quadratic Congruence of Composite Modulus modulo Even Multiple of an Odd Prime

by Prof B M Roy "Formulation of a Class of Standard Quadratic Congruence of Composite Modulus modulo Even-Multiple of an Odd Prime"

Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-1 , December 2020,

URL: https://www.ijtsrd.com/papers/ijtsrd38228.pdf

Paper URL : https://www.ijtsrd.com/mathemetics/applied-mathematics/38228/formulation-of-a-class-of-standard-quadratic-congruence-of-composite-modulus-modulo-evenmultiple-of-an-odd-prime/prof-b-m-roy

callforpapermathematics, mathematicsjournal, ugcapprovedjournalsinmathemetics

The author here in this paper presented formulation of solutions of a class of standard quadratic congruence of composite modulus modulo an even multiple of an odd prime. The established formula is tested and verified true by solving various numerical examples. The formulation works well and proved time saving. 

[ijtsrd]

RP 56 Reformulation of Solutions of a Standard Quadratic Congruence of Composite Modulus An Eighth Multiple of a Product of Two Odd Primes

by Prof B M Roy "RP-56: Reformulation of Solutions of a Standard Quadratic Congruence of Composite Modulus- An Eighth Multiple of a Product of Two Odd Primes"

Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-6 , October 2020,

URL: https://www.ijtsrd.com/papers/ijtsrd33407.pdf

Paper Url: https://www.ijtsrd.com/mathemetics/applied-mathematics/33407/rp56-reformulation-of-solutions-of-a-standard-quadratic-congruence-of-composite-modulus-an-eighth-multiple-of-a-product-of-two-odd-primes/prof-b-m-roy

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In this paper, the author considered a very general type of standard quadratic congruence of composite modulus an eighth multiple of product of two odd primes for reformulation of its solutions. The author’s first formulation was very simple but readers had to use many formulae for its solutions. Now the reformulation reduces the numbers of formulae for solutions. The discovered formula is justified and verified by using some required suitable numerical examples. The congruence is first time formulated. It is the merit of the paper. The existed method is complicated and time consuming. Now a time saving formulation is obtained. 

[ijtsrd]

Rp 135 Reformulation of Solutions of the Standard Quadratic Congruence of Composite Modulus A Product of Odd Prime Power Integer and Four

by Prof B M Roy "Rp-135: Reformulation of Solutions of the Standard Quadratic Congruence of Composite Modulus- A Product of Odd Prime-Power Integer and Four"

Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-5 , August 2020,

URL: https://www.ijtsrd.com/papers/ijtsrd33079.pdf

Paper Url :https://www.ijtsrd.com/mathemetics/applied-mathamatics/33079/rp135-reformulation-of-solutions-of-the-standard-quadratic-congruence-of-composite-modulus-a-product-of-odd-primepower-integer-and-four/prof-b-m-roy

callforpaperphysics, physicsjournal

In this paper, the author reformulated the solutions of the standard quadratic congruence of composite modulus a product of odd prime power integer and four. In the first formulation the solutions were obtained using different formulae. Now, a single formula is established for solutions. The formula is tested and verified using some illustrations. No need to use Chinese Remainder Theorem and solutions can now be obtained orally using the new formula. This is the merit of the paper. 

[ijtsrd]

RP 58 Formulation of Solutions of Standard Cubic Congruence of Composite Modulus A Product of Eight Multiple of an Odd Prime and Nth Power of Three

by Prof B M Roy "RP-58: Formulation of Solutions of Standard Cubic Congruence of Composite Modulus - A Product of Eight-Multiple of an Odd Prime & Nth Power of Three"

Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-4 , June 2020,

URL: https://www.ijtsrd.com/papers/ijtsrd31566.pdf

Paper Url :https://www.ijtsrd.com/mathemetics/applied-mathamatics/31566/rp58-formulation-of-solutions-of-standard-cubic-congruence-of-composite-modulus--a-product-of-eightmultiple-of-an-odd-prime-and-nth-power-of-three/prof-b-m-roy

ugcapprovedmanagementjournal, openaccessjournalofmanagement, paperpublicationinmanagement

In this paper, a standard cubic congruence of even composite modulus a product eight multiple of an odd prime and nth power of three, is considered for solutions. The congruence is studied and formulation of its solution is established. The formulation is done in two cases with different formula of solutions. Using the formula, the finding of solutions becomes easy and time saving. Formulation is the merit of the paper. 

[ijtsrd]

Rp 72 Formulation of Solutions of a Standard Cubic Congruence of Composite Modulus a Multiple of Four and Power of Three

by Prof B M Roy "Rp-72: Formulation of Solutions of a Standard Cubic Congruence of Composite Modulus-a Multiple of Four and Power of Three"

Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-3 , April 2020,

URL: https://www.ijtsrd.com/papers/ijtsrd30762.pdf

Paper Url :https://www.ijtsrd.com/mathemetics/other/30762/rp72-formulation-of-solutions-of-a-standard-cubic-congruence-of-composite-modulusa-multiple-of-four-and-power-of-three/prof-b-m-roy

ugclistedjournals, indexedjournal, paperpublication

In this study, a standard cubic congruence of composite modulus a multiple of four and power of three is considered. After a thorough study, formulation of the solutions of the said congruence are established in four different cases. It is found that the standard cubic congruence under consideration in case I has exactly three solutions for an odd positive integer and in case II, has six solutions for an even positive integer. In case III, it has nine solutions and in case IV, the congruence has exactly eighteen solutions. Formulations are the merit of the study.