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MATH / 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^nequiv 3pmod{13}, then what is the remainder when k …

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problem

Let nn be a positive integer and let kk be the number of positive integers less than 2n2^n that are invertible modulo 2n2^n. If $2^n\equiv 3\pmod{13}$, then what is the remainder when kk is divided by 1313?
Plain-text mathematical notation (without MathML)
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?
Original LaTeX notation
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 $13$?

level

Level 5

type

Number Theory

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Source and history

task_id
6ab01926-4ea1-53f4-aeac-dd74e22c5e2a
task_key
number~5ftheory--test--6ab01926-4ea1-53f4-aeac-dd74e22c5e2a
task_revision_id
1
config / split
number_theory / test

Official source

initial import