Hi this is simple question, but it's been troubling me for some time because I can't find anywhere what does it actually mean (algebra) -
$(a,b)=1$
is it GCD of those two values?
Asked
Active
Viewed 552 times
2
-
6Yes. This is standard notation for GCD. – walkar Feb 13 '15 at 17:43
-
and [a,b] is for LCM – Arashium Feb 13 '15 at 17:47
-
2As others have made clear, $(a,b)=1$ means the $\mathrm{gcd}$ of $a$ and $b$ is $1$; however, in general, the notation $(a,b)$ may mean something else--the context will make it clear what $(a,b)$ is supposed to mean. – Daniel W. Farlow Feb 13 '15 at 17:53
3 Answers
2
Yes, that means that $\operatorname{gcd}(a,b) = 1$, that the greatest common divisor among $a$ and $b$ is one. That is, that the numbers are coprime, or relatively prime.
The notation $a \perp b$ is also used to denote $\operatorname{gcd}(a,b) = 1$.
GFauxPas
- 5,047
2
The notation is commonly usd for the gcd, but it can also mean the ideal generated by $a$ and $b$.
That these notations clash has some sense as under certain conditions the ideal generated by $a$ and $b$ is just the ideal generated by a gcd of $a$ and $b$.
quid
- 42,135
0
It means that $a$ and $b$ are coprime, that their greatest common divisor (GCD) is $1$. But it's much better to write $\gcd(a, b) = 1$; if you're printing the paper out, what you lose in ink you gain in clarity.
Mr. Brooks
- 1,098