> 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:
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.