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

Home > Numbers
Square of an Odd (Posted on 2002-10-06) Difficulty: 2 of 5
Take any odd number and square it. It will invariably be a multiple of 8 plus 1. So (odd)^2=8n+1 where n is an integer. Show why this is always so. Also show what the pattern for n is.

See The Solution Submitted by martyn    
Rating: 3.1333 (15 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution | Comment 19 of 20 |
odd number is of the form 2*k+1
its square=4*(kČ+k)+1=4*k*(k+1)+1
k*(k+1) is definitely even bcoz either k or (k+1) is divisible by 2.
Let k*(k+1)=2*n for some n,
then square=8*n+1. Hence Proved

  Posted by Praneeth on 2007-08-01 13:11:24
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

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