Results 1 to 2 of 2

Math Help - Diophantine-type equation

  1. #1
    Senior Member
    Joined
    Nov 2007
    Posts
    329

    Diophantine-type equation

    Solve for integers:
    \frac 1x+\frac 1y=\frac 1{x-y}.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by james_bond View Post
    Solve for integers:
    \frac 1x+\frac 1y=\frac 1{x-y}.
    \frac{x+y}{xy} = \frac{1}{x-y} \implies x^2 - y^2 = xy

    Thus, x^2 - xy = y^2 \implies 4x^2-4xy = 4y^2 \implies 4x^2 - 4xy + y^2 = 5y^2

    Thus, (2x - y)^2 = 5y^2

    This is impossible.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Diophantine equation
    Posted in the Number Theory Forum
    Replies: 0
    Last Post: July 23rd 2011, 10:51 PM
  2. [SOLVED] diophantine equation
    Posted in the Number Theory Forum
    Replies: 0
    Last Post: January 11th 2011, 07:26 PM
  3. Diophantine Equation
    Posted in the Number Theory Forum
    Replies: 14
    Last Post: April 13th 2010, 06:00 PM
  4. Diophantine equation
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: November 21st 2009, 06:29 PM
  5. A diophantine equation
    Posted in the Number Theory Forum
    Replies: 28
    Last Post: June 23rd 2006, 05:19 AM

Search Tags


/mathhelpforum @mathhelpforum