Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems Abstract Algebra: Theory and Applications · Problem 6.5.22
Introduction to Cryptography — Thomas Judson
Mathematics — Abstract Algebra · euler-phi-function
Problem Let n = p 1 e 1 p 2 e 2 ⋯ p k e k n = p_1^{e_1} p_2^{e_2} \cdots p_k^{e_k} n = p 1 e 1 p 2 e 2 ⋯ p k e k p 1 , p 2 , … , p k p_1, p_2, \ldots, p_k p 1 , p 2 , … , p k ϕ ( n ) = n ( 1 − 1 p 1 ) ( 1 − 1 p 2 ) ⋯ ( 1 − 1 p k ) . \phi(n) = n\left(1 - \frac{1}{p_1}\right)\left(1 - \frac{1}{p_2}\right) \cdots \left(1 - \frac{1}{p_k}\right). ϕ ( n ) = n ( 1 − p 1 1 ) ( 1 − p 2 1 ) ⋯ ( 1 − p k 1 ) . gcd ( m , n ) = 1 \gcd(m,n) = 1 g cd( m , n ) = 1 ϕ ( m n ) = ϕ ( m ) ϕ ( n ) \phi(mn) = \phi(m)\phi(n) ϕ ( mn ) = ϕ ( m ) ϕ ( n ) Browse the problem library