Application of Fermat’s Little Theorem in Congruence Relation Modulo n

Abstract

According to Fermat's little theorem, for any p is a prime integer and gcdx,p=1, then the congruence xp-1≡1mod n is true, if we remove the restriction that gcdx,p=1, we may declarexp-1≡xmod p. For every integer x. Euler extended Fermat's Theorem as follows: if gcdx,p=1,then,where xÏ•n≡1mod n.Ï• is Euler's phi-function. Euler's theorem cannot be implemented for any every integers x in the same manners as Fermat’s theorem works; that is, the congruence xÏ•n+1≡xmod n is not always true. In this paper, we discussed the validation of congruence xÏ•n+1≡xmod n.

Authors and Affiliations

S. P. Behera, J. K. Pati, S. K. Patra, P. K. Raut

Keywords

Related Articles

Recommendations for the Development and Improvement of Immunoassays for the Detection of Host Antibodies to Biotechnology Goods

The majority of biopharmaceutical treatments generate some amount Allergic reaction to a foodstuff. In some instances, an immune reaction may have had serious consequences. And/or a loss of effectiveness. As a result, do...

A Review on the Detection and Classification of Glaucoma Disease Based on Transfer Learning

An eye infection is a condition affecting the eyes that can be caused by a bacterium, virus, or fungus. Numerous eye infections exist, such as glaucoma, cellulitis, keratitis, and conjunctivitis. A few of the symptoms ma...

Development of an AI-Driven Model for Advancing Software Engineering Practices

This work introduces the Fuzzy Specification Tree Model (FST), a general-purpose framework designed to enhance AI-assisted software engineering. The paper begins by examining the intricate interplay between software engi...

The Progression in the Agriculture Area By means of IoT

The agricultural industry plays an essential role in overcoming the food scarcity scenarios for food security globally in the rising population scenario. In the agricultural sector, mechanization has improved various cro...

An Overview on Solar Photovoltaic and Roof Top Application of IT

Since first oil embargo in 1973, the terms "energy crisis" and "energy security" have been constantly in the headlines. Concerns about environmental effects from fossil fuel-based power production have been a source of w...

Download PDF file
  • EP ID EP746537
  • DOI 10.55524/ijircst.2022.10.2.2
  • Views 31
  • Downloads 0

How To Cite

S. P. Behera, J. K. Pati, S. K. Patra, P. K. Raut (2022). Application of Fermat’s Little Theorem in Congruence Relation Modulo n. International Journal of Innovative Research in Computer Science and Technology, 10(2), -. https://europub.co.uk/articles/-A-746537