If $n=\frac{a}{b}$ , with $n, a$ and $b$ integers $( b ≠ 0)$, and with $a$ and $b$ coprimes, does $b=1$?

Question

If $n = { \dfrac{a}{b} }$ , with $n$ ${ \in }{ \mathbb{N} }$, $a$ ${ \in }$ ${ \mathbb{N} }$, and $b$ ${ \in }$ ${ \mathbb{N^*} }$ , and if $a$ and $b$ are coprime, then does $b$ $=$ $1$ ?

I can only see that as an option, but I'm not enirely sure. A little help ?

Thanks.

Answer 1

Yes, since $b\mid a$ and $b\mid b$ hence $b|\gcd(a,b)=1$, hence $b=1$.