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

Home > Numbers
Go for short! (Posted on 2005-04-19) Difficulty: 2 of 5
Looking at the "Square of an Odd" puzzle that asks to prove that the square of an odd number is always 1 more than a multiple of 8, a professor gave this four parts proof: "All odd numbers are of the form 8K+1, 8K+3, 8K+5 or 8K+7. Squaring these numbers produces 8M+1, 8M+9, 8M+25 or 8M+49, which are all of the form 8N+1. QED"

Another professor came by, and gave a single line proof. Can you manage it?

Note: no one who answered the original problem produced either the four parts solution, or the single line one.

  Submitted by e.g.    
Rating: 2.0000 (2 votes)
Solution: (Hide)
All odd numbers are 4K1, which squared produces 16K8K+1, which obviously is a multiple of 8, plus 1.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re: my waybroll2016-06-24 23:39:48
Solutionmy wayAdy TZIDON2012-08-07 12:55:59
Some ThoughtsIf two lines were allowed in the proof......K Sengupta2008-12-17 06:09:53
SolutionPuzzle SolutionK Sengupta2008-12-16 13:19:13
"computer" solutionDuncan Garp2005-06-04 05:34:12
SolutionSolutionMichael Cottle2005-04-19 18:29:51
SolutionAnother wayFederico Kereki2005-04-19 12:43:14
SolutionHow about this?Bractals2005-04-19 11:08:36
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 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information