Application of Fermat’s Little Theorem in Congruence Relation Modulo n
DOI:
https://doi.org/10.55524/Keywords:
Chinese Remainder theorem, Euler’s Function, Fermat’s little theorem, Primitive RootsAbstract
According to Fermat's little theorem, for any p is a prime integer and ������(��, ��) = 1, then the congruence ����−1 ≡ 1(������ �� )is true, if we remove the restriction that ������(��, ��) = 1, we may declare����−1 ≡ ��(������ ��). For every integer x. Euler extended Fermat's Theorem as follows: if ������(��, ��) = 1,then,where ����(��) ≡ 1(������ ��).�� 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 ����(��)+1 ≡ ��(������ ��) is not always true. In this paper, we discussed the validation of congruence ����(��)+1 ≡ ��(������ ��).
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