- #1

roam

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## Homework Statement

Let R be a ring and a be an element of R. Let [tex]S= \left\{ x \in R: ax=0_R \right\}[/tex]. S is a subring of R.

Let [tex]R= \mathbb{Z}_{2000}[/tex] and [tex]a=850[/tex]. Determine the elements of the subring S as defined previously. How many elements are in S?

## The Attempt at a Solution

The elements of the subring S will be elements x from [tex]\mathbb{Z}_{2000}[/tex] such that [tex]850.x=0_R[/tex].

And I think since 850x=0-5000n, [tex]x= \frac{2000}{850} n = \frac{40}{21} n[/tex] then

n=k.21

But what I do I need to do to find the number of elements in S? Is there a quick way of finding this?