The Order Divisibility Property states that if a(adsbygoogle = window.adsbygoogle || []).push({}); ^{n}= 1 (mod p), then the order e_{p}(a) of a (mod p) divides n.

How can I go about proving this?

Additionally, if a is relatively prime to p, when does the congruence a^{m}= a^{n}(mod p) hold? Is there a proof for this as well?

Thanks!!

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# Proof of the Order Divisibility Property

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