Volume- 10
Issue- 2
Year- 2022
DOI: 10.55524/ijircst.2022.10.2.2 |
DOI URL: https://doi.org/10.55524/ijircst.2022.10.2.2
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This is an Open Access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0) (http://creativecommons.org/licenses/by/4.0)
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S. P. Behera , J. K. Pati, S. K. Patra, P. K. Raut
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
.
[1] Niven, Zuckerman and Montgomery 1991, An Introduction to the Theory of Numbers, 4th edition (New York: Wiley).
[2] S.P Behera and A.C Panda, Nature Of Diophantine Equation 4x +12y= z2, International Journal of Innovative Research in Computer Science and Technology (IJIRCST), Vol.09 (6) (2021), 11-12.
[3] Diamond F, Shurman J. A first course in modular forms. Springer; 2005.
[4] N. Freitas and S. Siksek, The asymptotic Fermat’s last theorem for five-sixths of real quadratic fields, Compos. Math.Vol18 (8) (2015) 1395–1415
[5] G. Turcas, On Fermat’s equation over some quadratic imaginary number fields, Res. Number Theory 4 (2018) 24
[6] G. Turcas, On Fermat’s equation over some quadratic imaginary number fields, Res. Number Theory 4 (2018) 24
Assistant Professor of Mathematics, C.V.Raman Global University, Bhubaneswar, Odisha, India
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