Definition:Coprime/Notation
Jump to navigation
Jump to search
Definition
Let $a$ and $b$ be objects which in some context are coprime, that is, such that $\gcd \set {a, b} = 1$.
Then the notation $a \perp b$ is preferred on $\mathsf{Pr} \infty \mathsf{fWiki}$.
If $\gcd \set {a, b} \ne 1$, the notation $a \not \!\! \mathop \perp b$ can be used.
As stated in 1994: Ronald L. Graham, Donald E. Knuth and Oren Patashnik: Concrete Mathematics: A Foundation for Computer Science (2nd ed.), section $4.5$:
- This concept is so important in practice, we ought to have a special notation for it; but, alas, number theorists haven't agreed on a very good one yet. Therefore we cry: "HEAR US, O MATHEMATICIANS OF THE WORLD! LET US NOT WAIT ANY LONGER! WE CAN MAKE MANY POPULAR FORMULAS CLEARER BY ADOPTING A NEW NOTATION NOW! LET US AGREE TO WRITE '$m \perp n$' AND TO SAY "$m$ is prime to $n$," IF $m$ AND $n$ ARE RELATIVELY PRIME.
Can't say it more clearly than that.