## question on slopes and intersects

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• Hi, I have a question which is related to factoring composite numbers, although why may not be obvious at first. I have a (straight) line x1,y1 to x2,y2 where
Message 1 of 2 , Sep 6 5:35 PM
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Hi,

I have a question which is related to factoring composite numbers,
although why may not be obvious at first.

I have a (straight) line x1,y1 to x2,y2 where x1 and x2 are whole
numbers and y1 and y2 are not.

My question is, can I calculate the first time the line intersects an
x,y coordinate where both x and y are whole numbers.

Kevin.
• Hi Kevin, This shouldn t be too hard. simply shift your x,y axis so that (x1,y1)=(0,0) you can then express your line as y=mx (m=y2/x2) multiply by appropriate
Message 2 of 2 , Sep 8 1:56 AM
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Hi Kevin,
This shouldn't be too hard.
so that (x1,y1)=(0,0)
you can then express your line as
y=mx (m=y2/x2)
multiply by appropriate numberq so that qy2 and qx2 are integer
let x=qx2 and you will get an iteger y
shift you axes back.
e.g
x1=1, y1=2
x2=5/2 y2=13/3
shift axes
x1=0,y1=0
x2=3/2,y2=7/3
y= (7/3)/(3/2)x
y= (14/9)x
x=9 ==> y=14
shift back (i.e add 1 to x and 2 to y)
x=10,y=16 are integer cordinates on the line that pases through
(1,2) and (2.5,4.3...)

Hope this helps
Cheers
Ken
--- In primenumbers@yahoogroups.com, "Kevin Acres" <research@r...>
wrote:
> Hi,
>
> I have a question which is related to factoring composite numbers,
> although why may not be obvious at first.
>
> I have a (straight) line x1,y1 to x2,y2 where x1 and x2 are whole
> numbers and y1 and y2 are not.
>
> My question is, can I calculate the first time the line intersects
an
> x,y coordinate where both x and y are whole numbers.
>
> Kevin.
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