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Let $n$ be a positive integer and let $k$ be the number of positive integers less than $2^n$ that are invertible modulo $2^n$. If $2^n \equiv 3\pmod{13}$, then what is the remainder when $k$ is divided by $13$?

 Sep 12, 2021
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The remainder when k is divided by 13 is 10.

 Sep 12, 2021

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