Date: Dec 3, 2012 2:36 PM
Author: Dave L. Renfro
Subject: Re: An Algebra 2 Test
Dave L. Renfro wrote:

http://mathforum.org/kb/message.jspa?messageID=7897783

> I only have a few moments before I need to leave to tutor

> someone, but here's a somewhat silly one off the top of

> my head:

>

> Determine the exact value of a^2 - b^2 if

>

> a = 7.0241132301442003123012230341430201

> b = 6.0241132301442003123012230341430201

>

> Calculators are allowed.

I posted this about 2 months ago, and at the time I only

considered it to be an easy level math contest type of problem

with no applications other than being a contrived application

of the difference of squares formula. However, this weekend

I happened to come across the following article:

Carl Pomerance, "A tale of two sieves", Notices of the American

Mathematical Society 43 #12 (December 1996), 1473-1485.

http://www.ams.org/notices/199612/pomerance.pdf

This article is essentially about how a version of the

trick above leads to nontrivial results involving factoring

large integers, which (as most you probably know) is hugely

important in the encryption of data.

In particular, look at the right column on p. 1474.

Dave L. Renfro