IJIRCSTJournal International Journal of Innovative Research in Computer Science and Technology I S Volume 10 Issue 2 Mathematics English March - April 2022 N N Y 2022 03 24 Computer Sciences Application of Fermat’s Little Theorem in Congruence Relation Modulo n English Y 7 9 S. P. Behera English Y J. K. Pati English N S. K. Patra English N P. K. Raut English N https://doi.org/10.55524/ijircst.2022.10.2.2 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. English Chinese Remainder theorem, Euler’s Function, Fermat’s little theorem, Primitive Roots https://ijircst.org/abstract.php?article_id=816