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

Home > Numbers
Subtle Summed Squares (Posted on 2007-05-18) Difficulty: 3 of 5
Suppose a number N can be written as P times Q times R times..., where all of P, Q, R... can each be written as the sum of two perfect nonzero squares.

Show that in this case N itself can also be written as the sum of two perfect squares.

See The Solution Submitted by Old Original Oskar!    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Not so fast! | Comment 4 of 6 |
(In reply to Not so fast! by Steve Herman)

What seems to be a flaw at first is not.  The numbers P, Q, ... are expressable as the sum of non-zero squares.  The thing that was to be shown almost makes a point of not requiring the squares summing to N be non-zero.

If it did require the square summing to N be non-negative, then an exception occurs.  N cannot be a perfect square unless it is the square of a number that can be written as the sum of two squares in two different ways.


  Posted by Jer on 2007-05-21 12:26:28
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