Thread: Help solve this

Show that for any integer m>1, a^m≡a^(m-φ(m))mod(m).Help

What is ?

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.

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.

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.