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Euler–Fermat theorem

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1: 27.16 Cryptography
Thus, y x r ( mod n ) and 1 y < n . … By the EulerFermat theorem (27.2.8), x ϕ ( n ) 1 ( mod n ) ; hence x t ϕ ( n ) 1 ( mod n ) . …
2: 27.2 Functions
This is the number of positive integers n that are relatively prime to n ; ϕ ( n ) is Euler’s totient. If ( a , n ) = 1 , then the EulerFermat theorem states that …
3: 27.8 Dirichlet Characters
For any character χ ( mod k ) , χ ( n ) 0 if and only if ( n , k ) = 1 , in which case the EulerFermat theorem (27.2.8) implies ( χ ( n ) ) ϕ ( k ) = 1 . …
4: 24.17 Mathematical Applications
§24.17(iii) Number Theory
Bernoulli and Euler numbers and polynomials occur in: number theory via (24.4.7), (24.4.8), and other identities involving sums of powers; the Riemann zeta function and L -series (§25.15, Apostol (1976), and Ireland and Rosen (1990)); arithmetic of cyclotomic fields and the classical theory of Fermat’s last theorem (Ribenboim (1979) and Washington (1997)); p -adic analysis (Koblitz (1984, Chapter 2)). …