# Help solve this

• May 7th 2010, 07:54 AM
ogajawasungu
Help solve this
Show that for any integer m>1, a^m≡a^(m-φ(m))mod(m).Help
• May 7th 2010, 08:27 AM
Bruno J.
What is $\displaystyle a^{\phi(m)}\mod m$?
• May 8th 2010, 03:31 AM
ogajawasungu
Help solve this
For any integer m>1,φ(m) is the number of integers not greater than m and are relatively prime to m.I think I can re frame my question if you don't understand the former;For any integer m>1,show that m divides a^m-a^(m- φ(m)) for all integers a.
• May 8th 2010, 05:00 AM
Bacterius
Quote:

Originally Posted by ogajawasungu
For any integer m>1,φ(m) is the number of integers not greater than m and are relatively prime to m.I think I can re frame my question if you don't understand the former;For any integer m>1,show that m divides a^m-a^(m- φ(m)) for all integers a.

I think Bruno J. was trying to hint you a property of this function. Think of Euler's Generalization.
• May 8th 2010, 05:34 AM
ogajawasungu
I thought of it earlier,but because Euler's generalization requires that (a,m)=1,this kind of problem became a nightmare to me.I also tried by induction proof and got stuck.