S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
It is currently Fri, 24 Oct 2014 08:41:41 UTC

All times are UTC [ DST ]




Post new topic Reply to topic  [ 3 posts ] 
Author Message
 Post subject: Not a square to be found
PostPosted: Wed, 18 Jan 2012 01:33:37 UTC 
Offline
Moderator
User avatar

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 14154
Location: Austin, TX
Here's a fun little problem. Show that:

11, 111, 1111, 11111, 111111, ... has no perfect squares on the list.

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination


Top
 Profile  
 
PostPosted: Wed, 18 Jan 2012 06:38:51 UTC 
Offline
S.O.S. Oldtimer

Joined: Fri, 27 Jul 2007 10:17:26 UTC
Posts: 279
Location: Chandler, AZ, USA
This might not be the most elegant proof:

Spoiler:
The last two digits of n^2 can only be

01, 04, 09, 16, 25, 36, 49, 64, 81, 00, 21, 44, 69, 96, 25, 56, 89, 24, 61, 00, 41, 84, 29, 76, 25

We only need to list the first 25 squares, since (50x \pm n)^2 = 100M + n^2.

11 is not on that list.

I wanted to try something a little slicker with 1111... = \frac{10^n - 1}{9}. If n is even, it is fairly obvious, but I didn't have time to work out the case of n being odd.


Edit (outermeasure): hiding.


Top
 Profile  
 
PostPosted: Wed, 18 Jan 2012 06:40:39 UTC 
Offline
Moderator
User avatar

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 14154
Location: Austin, TX
alstat wrote:
This might not be the most elegant proof:

The last two digits of n^2 can only be

01, 04, 09, 16, 25, 36, 49, 64, 81, 00, 21, 44, 69, 96, 25, 56, 89, 24, 61, 00, 41, 84, 29, 76, 25

We only need to list the first 25 squares, since (50x \pm n)^2 = 100M + n^2.

11 is not on that list.

I wanted to try something a little slicker with 1111... = \frac{10^n - 1}{9}. If n is even, it is fairly obvious, but I didn't have time to work out the case of n being odd.


Hint:

Spoiler:
All the numbers on my list are odd
.

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination


Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 3 posts ] 

All times are UTC [ DST ]


Who is online

Users browsing this forum: No registered users


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum

Search for:
Jump to:  
Contact Us | S.O.S. Mathematics Homepage
Privacy Statement | Search the "old" CyberBoard

users online during the last hour
Powered by phpBB © 2001, 2005-2011 phpBB Group.
Copyright © 1999-2013 MathMedics, LLC. All rights reserved.
Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA