All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
Call 911 (Posted on 2018-08-03) Difficulty: 4 of 5
x^2 + 3xy + 2*911x + 2*911y +911^2 = 0.

Solve the bolded equation for an integer couple (x,y)

See The Solution Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution Comment 2 of 2 |
I was hoping to find an elegant trick using x+y+911, but nope.  At least the equation can be solved for y without radicals.

y = -(3x+3644)/9 - (829921/(3x+1822))/9

829921 has six integer factors: 1, -1, 911, -911, 829921, -829921.  Equating each of these to 3x+1822 yields three integer possibilities for x: -607, -911, and 276033.  This in turn yields three integer couples (-607,-92416), (-911,0), and (276033,-92416).

  Posted by Brian Smith on 2018-08-11 18:34:34
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2020 by Animus Pactum Consulting. All rights reserved. Privacy Information