proof of a corollary to Euler-Fermat theorem


This is an easy consequence of Euler-Fermat theorem:

Let di,mi be defined as in the parent entry. Then gcd(a,ms)=1 and Euler’s theorem implies:

aϕ(ms)1modms

Note also that each of ds-1,,d0 divides a, so di divides as, so di divides aϕ(ms)+s-as. Also, gcd(di,ms)=1 and msdi=m. Therefore:

aϕ(ms)+sasmodm

which is what the corollary claimed.

Title proof of a corollary to Euler-Fermat theorem
Canonical name ProofOfACorollaryToEulerFermatTheorem
Date of creation 2013-03-22 14:23:20
Last modified on 2013-03-22 14:23:20
Owner alozano (2414)
Last modified by alozano (2414)
Numerical id 5
Author alozano (2414)
Entry type Proof
Classification msc 11-00