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

A New Residual Convolutional Neural Network-Based Speech Improvement

Among the most crucial methods for denoising a noisy voice signal and enhancing its quality is speech enhancement. This study makes use of Adaptive Residual Neural Network technique to reduces maximum off background nois...

Near-Merger Electromagnetic Emission from Super massive Binary Black Holes

The first accelerated prediction involves infrared waves from the shielding fluid of a massive bipolar neutron stars system on the verge of merging. Using a ray-tracing approach to thread data from just a universal veloc...

Twitter Data Classification by Applying and Comparing Multiple Machine Learning Techniques

Having an average of five hundred million tweets sent out per day, twitter has become one of the largest platforms of data analysis for the researchers. Previously, various researches have been conducted on twitter data...

An Overview of Device-To-Device Communication in Cellular Networks

Gadget to-Device (D2D) correspondence was first recommended as another worldview for further developing organization execution in cell organizations. New use-cases for D2D correspondences in cell networks have arisen bec...

A Review Paper on Slit Erosion

The eruptive wearing of hydrokinetic blades is a complex operation impacted by a number of elements such as silt size, softness and concentrations, flow speed, and foundation materials properties. As eruptive attrition a...

Download PDF file
  • EP ID EP746537
  • DOI 10.55524/ijircst.2022.10.2.2
  • Views 40
  • 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