MathDB

D 12

Source:

May 25, 2007

modular arithmeticfloor functionabstract algebranumber theoryrelatively primegroup theoryCongruences

Problem Statement

Suppose that

m>2

, and let

P

be the product of the positive integers less than

m

that are relatively prime to

m

. Show that

P \equiv -1 \pmod{m}

m=4

p^n

, or

2p^{n}

, where

p

is an odd prime, and

P \equiv 1 \pmod{m}

otherwise.