Competition problem — Number theory

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Number theory Difficulty 5.9 AIME, harder Prove it

9. Show that if $a$ is an integer relatively prime to the positive integer $m$ and $\operatorname{ord}_{m} a=s t$ , then $\operatorname{ord}_{m} a^{t}=s$ .

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.