MathDB

D 4

Source:

May 25, 2007

modular arithmeticblogsCongruences

Problem Statement

Let

n

be a positive integer. Prove that

n

is prime if and only if

{{n-1}\choose k}\equiv (-1)^{k}\pmod{n}

for all

k \in \{ 0, 1, \cdots, n-1 \}