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For how many integers $a$ satisfying $1 \le a \le 23$ is it true that $a^{-1} \equiv a \pmod{24}$?

Mar 24, 2020

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Sorry I was going to post an answer to this, but it got deleted when I tried submitting :(. I only got through part of this, but I'll try uploading a new answer tomorrow. In the meantime, try searching up "bezouts identity" and its relation with fractional modulo. What can you immediately realize won't satisfy the requirements of the given expression?(Hint: it has something to do with the denominators being coprime to the modulus).

Mar 24, 2020
#2
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Also please make sure to properly format your question! I'd check this site out for reference. It'll help you understand some properties and conditions of fractional modulo

https://math.stackexchange.com/questions/864568/is-it-possible-to-do-modulo-of-a-fraction

jfan17  Mar 24, 2020