Prove that if m and n are positive integers and if ab ≡ 1 (mod m) and

a^n ≡ 1 (mod m), then b^n ≡ 1 (mod m).

Any help would be greatly appreciated! I am lost with this one but I probably am just missing a very simple step. Thanks!

Printable View

- Jan 20th 2010, 11:20 AMFatherMikeCongruence Proof
Prove that if m and n are positive integers and if ab ≡ 1 (mod m) and

a^n ≡ 1 (mod m), then b^n ≡ 1 (mod m).

Any help would be greatly appreciated! I am lost with this one but I probably am just missing a very simple step. Thanks! - Jan 20th 2010, 12:30 PMDinkydoe
Given is mod m. This implies that mod m.

Thus if mod n what does this say about mod m? - Jan 20th 2010, 12:30 PMDrexel28