User Name Remember Me? Password

 Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

 July 8th, 2019, 11:42 PM #1 Senior Member   Joined: Dec 2015 From: somewhere Posts: 636 Thanks: 91 Solve for integers Find all pairs $\displaystyle (x,y)$ such that $\displaystyle x+y=xy$, where $x,y$ are integers. Last edited by skipjack; July 9th, 2019 at 02:22 AM. July 9th, 2019, 01:36 AM   #2
Math Team

Joined: May 2013
From: The Astral plane

Posts: 2,267
Thanks: 934

Math Focus: Wibbly wobbly timey-wimey stuff.
Quote:
 Originally Posted by idontknow Find all pairs $\displaystyle (x,y)$ such that $\displaystyle x+y=xy \;$ , where x,y integers .
Solving for y:
$\displaystyle y = \dfrac{x}{x - 1}$

If y is to be an integer that means that x must be a multiple of x - 1. The only possibilities are x = 0, giving y = 0 and x = 2, giving y = 2.

So the solution set is (x, y) = {(0, 0), (2, 2)}.

-Dan Tags integers, solve Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post idontknow Elementary Math 4 June 2nd, 2019 06:23 PM yo79 Math Events 4 March 17th, 2013 12:50 AM ultramegasuperhyper Number Theory 4 May 24th, 2011 09:19 PM Sara so Number Theory 3 November 12th, 2010 12:18 PM cafegurl Elementary Math 3 January 7th, 2009 07:21 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top      