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RE: [PrimeNumbers] Question on slopes and intersects

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  • Milton Brown
    Your problem as stated has no solution. Consider the line y = x*sqrt(2). Any point (x1,y1) on the line, can not have both x and y be whole numbers. Perhaps
    Message 1 of 3 , Sep 7, 2004
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      Your problem as stated has no solution.

      Consider the line y = x*sqrt(2).
      Any point (x1,y1) on the line, can not have
      both x and y be whole numbers.

      Perhaps you wish to re-state your problem.

      Milton L. Brown
      miltbrown@...


      > [Original Message]
      > From: Kevin Acres <research@...>
      > To: <primenumbers@yahoogroups.com>
      > Date: 9/6/2004 5:35:42 PM
      > Subject: [PrimeNumbers] question on slopes and intersects
      >
      > 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.
      >
      >
      >
      >
      > Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
      > The Prime Pages : http://www.primepages.org/
      >
      >
      > Yahoo! Groups Links
      >
      >
      >
      >
    • Kevin Acres
      Hi Milton, Thanks for the response. I should add the clarification that y1 and y2 even though not whole numbers are also not irrational. So eventually the
      Message 2 of 3 , Sep 7, 2004
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        Hi Milton,

        Thanks for the response. I should add the clarification that y1 and y2
        even though not whole numbers are also not irrational. So eventually the
        line will intersect an x,y coordinate where both are whole numbers, I just
        don't know how to calculate this.

        Kevin.

        At 01:05 PM 8/09/2004, Milton Brown wrote:

        >Your problem as stated has no solution.
        >
        >Consider the line y = x*sqrt(2).
        >Any point (x1,y1) on the line, can not have
        >both x and y be whole numbers.
        >
        >Perhaps you wish to re-state your problem.
        >
        >Milton L. Brown
        >miltbrown@...
        >
        >
        > > [Original Message]
        > > From: Kevin Acres <research@...>
        > > To: <primenumbers@yahoogroups.com>
        > > Date: 9/6/2004 5:35:42 PM
        > > Subject: [PrimeNumbers] question on slopes and intersects
        > >
        > > 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.
        > >
        > >
        > >
        > >
        > > Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
        > > The Prime Pages : http://www.primepages.org/
        > >
        > >
        > > Yahoo! Groups Links
        > >
        > >
        > >
        > >
      • trilliwig
        ... eventually the ... I just ... This doesn t involve factoring; all you have to do is write the slope of the line as a fraction in lowest terms, which can be
        Message 3 of 3 , Sep 7, 2004
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          --- In primenumbers@yahoogroups.com, Kevin Acres <research@r...> wrote:
          > I should add the clarification that y1 and y2
          > even though not whole numbers are also not irrational. So
          eventually the
          > line will intersect an x,y coordinate where both are whole numbers,
          I just
          > don't know how to calculate this.

          This doesn't involve factoring; all you have to do is write the slope
          of the line as a fraction in lowest terms, which can be done with a
          gcd computation.

          Sam
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