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question on slopes and intersects

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  • Kevin Acres
    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.
    • Ken Davis
      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.
        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 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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