Application of Fermat’s Little Theorem in Congruence  Relation Modulo n

S P  Behera; J K Pati; S  K Patra; P K Raut

doi:10.55524/

Authors

S P Behera Assistant Professor of Mathematics, C.V.Raman Global University, Bhubaneswar, Odisha, India Author
J K Pati Associate Professor of Mathematics, C.V.Raman Global University, Bhubaneswar, Odisha, India Author
S K Patra MSc Project Scholar, C.V. Raman Global University, Bhubaneswar, Odisha, India Author
P K Raut Research Scholar, C.V. Raman Global University, Bhubaneswar, Odisha, India Author

DOI:

https://doi.org/10.55524/

Keywords:

Chinese Remainder theorem, Euler’s Function, Fermat’s little theorem, Primitive Roots

Abstract

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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References

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