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From: Ted Schuerzinger <fe...@hughes.spam>
Newsgroups: alt.math.recreational,rec.puzzles
Subject: Re: Are these numbers known?
Date: Mon, 5 Dec 2011 09:24:20 -0500
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On Mon, 5 Dec 2011 13:13:43 +0000 (UTC), Willem wrote:

> No idea, but it seems to hinge on there being no carry in the
> multiplications, so one would guess it stops after a while.
> Perhaps there are outliers that don't depend on no carry.

It looks to me as though 
1 [insert arbitray number of 0's] 2 and 
1 [insert arbitray number of 0's] 3

won't have any carries:

(10^n + 2) ^ 2 = 10^2n + 4 * 10^n + 4
(2*10^n + 1) ^ 2 = 4 * (10^2n) + 4 * 10^n + 1

Those should be the reverse of each other.

-- 
Ted S.
fedya at hughes dot net
Now blogging at http://justacineast.blogspot.com