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I came across the following definition of the set on this web page

image

But what is $\operatorname{syt}$?

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  • $\begingroup$ Can you give context for this definition? Where did you see it originally? $\endgroup$
    – Mnifldz
    Apr 22, 2016 at 19:51
  • $\begingroup$ See the edit submitted one second after your comment ;) $\endgroup$
    – marmistrz
    Apr 22, 2016 at 19:51
  • $\begingroup$ This only shows the page I was reading ;( $\endgroup$
    – marmistrz
    Apr 22, 2016 at 20:13

2 Answers 2

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After a bit of poking around, I found the same result as @SiongthyeGoh, but not from a mathematical P.O.V:

From The Census of Mathematical Notations:

On the Helsinki University of Technology, Department of Mathematics website, we find that they use syt instead of $\gcd$, and it is called 'Suurin yhteinen tekijä' in a Finnish context.

Also find syt in Wikipedia. Usually at university level notation (a,b) is used for greatest common divisor of numbers a and b instead of letter combination syt. For example see Lecture notes by Pentti Haukkanen at University of Tampere.

For further reference, here is the link to the webpage quoted. As you might expect, it supposedly (I don't speak Finnish) translates somewhat literally to..."greatest common divisor"

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I believe it is just a typo. syt is just gcd.

\begin{align*} A_d &= \left\{ x: 1 \leq x \leq n\text{ and } gcd(x,n)=d \right\}\\ &= \left\{ dx': 1 \leq x' \leq n/d \text{ and } gcd(dx',n)=d \right\}\\ &= \left\{ dx': 1 \leq x' \leq n/d \text{ and } gcd(x',n/d)=1 \right\}.\\ \end{align*}

We can see that the set above have the same cardinality with the set

$$A_d'=\left\{ x: 1 \leq x \leq n/d \text{ and } gcd(x,n/d)=1 \right\}.$$

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