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# Number Theory

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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 = 5 (mod 15), then what is the remainder when k is divided by 15?

May 30, 2021

The question is wrong, no integer solutions exist to $2^n\equiv 5\pmod{15}$.