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MATH / Let n be the number of integers m in the range 1≤m≤8 such that gcd(m,8)=1. What is the remainder when 3^(n) is divided by 8?

Problem

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problem

Let nn be the number of integers mm in the range 1≤m≤81\le m\le 8 such that gcd(m,8)=1\text{gcd}(m,8)=1. What is the remainder when 3n3^n is divided by 88?
Plain-text mathematical notation (without MathML)
Let n be the number of integers m in the range 1≤m≤8 such that gcd(m,8)=1. What is the remainder when 3^(n) is divided by 8?
Original LaTeX notation
Let $n$ be the number of integers $m$ in the range $1\le m\le 8$ such that $\text{gcd}(m,8)=1$. What is the remainder when $3^n$ is divided by $8$?

level

Level 2

type

Number Theory

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Source and history

task_id
aaef8cfb-432c-52c2-a228-712ebed475a7
task_key
number~5ftheory--test--aaef8cfb-432c-52c2-a228-712ebed475a7
task_revision_id
1
config / split
number_theory / test

Official source

initial import