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

Dave L. Renfro wrote:

> 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.

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