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

Home > Just Math
Sum the integers, get squares? (Posted on 2007-04-05) Difficulty: 2 of 5
Can the sum of any 2112 consecutive positive integers be a perfect square?

See The Solution Submitted by K Sengupta    
Rating: 2.0000 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution solution | Comment 3 of 5 |

x + (x+1) + ... + (x+2111) = (2x+2111) * 1056

(2x+2111) is odd (has no factor of 2)

2 appears as a factor in 1056 (and therefore the whole total), five times, which is odd, so the 2's can't be separated equally into two equal factors (that being what a square root is).

  Posted by Charlie on 2007-04-05 10:25:45
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 (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information