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

Home > Just Math
Infinitely Diophantine (Posted on 2016-06-10) Difficulty: 3 of 5
Each of X, Y and Z is a positive integer > 1 such that:

(X2 + 1) (Y2 + 1) = (Z2 + 1)

Does there exist an infinite number of solutions to the above equation?
Give reasons for your answer.

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
No Subject Comment 2 of 2 |
From the equation comes
(xy)^2 + x^2 + y^2 = z^2

(xy)^2 + n^2 + 2nxy is a square for each value of n

Then when y=2x^2 or x=2y^2 z^2 will be square

For ex x=7 2x^2=98 Then if y=98, z will be square. For ex y=98
(7^2+1)(98^2+1)=693^2+1
Edited on June 11, 2016, 12:52 pm
  Posted by armando on 2016-06-11 11:04:10
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 (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information