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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 \(2^n=3\) (mod 13), then what is the remainder when \(k\) is divided by 13?

 Feb 24, 2021
 #1
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Turns out the answer is 8.

 Feb 24, 2021
 #2
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2^n mod 13 ==3

 

n ==4  and k==15

 

15 mod 13 == 2

 Feb 24, 2021

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