# What does $(a_i,m)=1$ mean in number theory?

I believe it means the greatest common divisor of $a_i$ and $m$ is $1$, meaning $a_i$ and $m$ are co-prime, but I want to be sure. Here is the context:

A reduced residue system modulo $m$ is a set of integers $a_1,...,a_k$ such that if $i \neq j$ and $(a_i,m)=1$, $a_i \not\equiv a_j \mod m$...

• It is indeed an old notation for the gcd (the one I used to use, which probably tells something about my age), the modern one would be $\gcd(a_{i}, m)$. – Andreas Caranti Feb 6 '16 at 17:33
• @AndreasCaranti As I suspected, thank you. – Agnostic Atheist Feb 6 '16 at 17:33
• That's exactly what it means. The notation should probably be defined in the book somewhere. I thought the notation was more universal than it is so it's best on these boards to specify gcd(a,b) – fleablood Feb 6 '16 at 17:34
• Really? When did $\gcd(a,b)$ become more common? I didn't know that (a,m) was no longer the norm. I was wondering why so few people here used it. – fleablood Feb 6 '16 at 17:35