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

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- May 7th 2010, 07:54 AMogajawasunguHelp solve this
Show that for any integer m>1, a^m≡a^(m-φ(m))mod(m).Help

- May 7th 2010, 08:27 AMBruno J.
What is $\displaystyle a^{\phi(m)}\mod m$?

- May 8th 2010, 03:31 AMogajawasunguHelp 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 AMBacterius
- May 8th 2010, 05:34 AMogajawasungu
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.