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

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  • EP ID EP746537
  • DOI 10.55524/ijircst.2022.10.2.2
  • Views 43
  • 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