Competition problem — Number theory

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Number theory Difficulty 5.9 AIME, harder Prove it

5. Show that if $\bar{a}$ is an inverse of $a$ modulo $n$ , then $\operatorname{ord}_{n} a=\operatorname{ord}_{n} \bar{a}$ .

Solution

None

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.