Application of Fermat’s Little Theorem in Congruence Relation Modulo n
Journal Title: International Journal of Innovative Research in Computer Science and Technology - Year 2022, Vol 10, Issue 2
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
- EP ID EP746537
- DOI 10.55524/ijircst.2022.10.2.2
- Views 20
- Downloads 0
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