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 $8$?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
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 $8$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
1
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 $8$?
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