MathDB
prime cirterion, \phi (n) divides (n - 1) and (n + 1) divides \sigma (n)

Source: Indian Postal Coaching 2008 set 4 p2

May 25, 2020
number theoryprimesprimeprime numbersdivides

Problem Statement

Prove that an integer n2n \ge 2 is a prime if and only if ϕ(n)\phi (n) divides (n1)(n - 1) and (n+1)(n + 1) divides σ(n)\sigma (n).
[Here ϕ\phi is the Totient function and σ\sigma is the divisor - sum function.]
nn is squarefree