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

Home > Just Math
Perfect Squares (Posted on 2003-04-05) Difficulty: 5 of 5
Show that the numbers of the form:

444444....4444888888....8889

[Where there are 'k' Fours, '(k-1)' Eights and 'Exactly One' 9],

are always perfect squares.

(For example the sequence of numbers: 49, 4489, 444889, ....etc. and so on are always perfect squares).

See The Solution Submitted by Ravi Raja    
Rating: 4.0000 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: solution | Comment 3 of 10 |
(In reply to solution by Charlie)

Charlie, suppose that DJ did not note that the square roots of the given sequence of numbers are of the form 7, 67, 667, 6667, ....etc. then how would you proceed to prove the numbers of the given form to be perfect squares ?
  Posted by Ravi Raja on 2003-04-06 04:12:57

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 (8)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information