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

Home > Just Math
A Pythagorean piglet (Posted on 2012-09-22) Difficulty: 3 of 5

Finding solutions to x2- b2=b2-1 is a bit too easy these days, so let b itself be the multiple of a square, say, yz2

For both y>1 and z>1, prove that y is not a square, or find a counter-example.

See The Solution Submitted by broll    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Oinking solution. | Comment 1 of 4
You want b = yz^2 where y is not a square, but if y were a square, say y = a^2 then you'd have b= a^2*z^2 = (az)^2 which is a square not the multiple of a square as sought.

This proves that y cannot be a square, so there will be no counterexamples.  Now to find if any solutions actually exist.

I found the first 3 values of b (5, 29, 169) and put them in OEIS which returned http://oeis.org/A001653
The sequence contains 195025 which is 7801*5^2

  Posted by Jer on 2012-09-25 16:17:25
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 (5)
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