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 Post subject: Not a square to be foundPosted: Wed, 18 Jan 2012 01:33:37 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 15563
Location: Austin, TX
Here's a fun little problem. Show that:

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

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 Post subject: Re: Not a square to be foundPosted: Wed, 18 Jan 2012 06:38:51 UTC
 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 can only be

We only need to list the first 25 squares, since .

is not on that list.

I wanted to try something a little slicker with . If is even, it is fairly obvious, but I didn't have time to work out the case of being odd.

Edit (outermeasure): hiding.

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 Post subject: Re: Not a square to be foundPosted: Wed, 18 Jan 2012 06:40:39 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 15563
Location: Austin, TX
alstat wrote:
This might not be the most elegant proof:

The last two digits of can only be

We only need to list the first 25 squares, since .

is not on that list.

I wanted to try something a little slicker with . If is even, it is fairly obvious, but I didn't have time to work out the case of being odd.

Hint:

Spoiler:
All the numbers on my list are odd
.

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