# Congruence of rectangles? please help

1. Jun 28, 2010

### numbthenoob

I'm trying to find more information on a corollary to the difference of squares principle in integer factorization, but I don't know what it's called and the search terms I've tried just return irrelevant results. Does anyone know what the official names of the following observations are?

1) Given that n2-a2 = (n-a)(n+a), it follows that (n2+cn)-(a2+ca) = (n-a)(n+a+c).

2) Any two squares are congruent modulo the sum and the differences of their roots. How do you refer to the idea that n(n+c) is congruent to a(a+c) modulo n-a, a-n & n+a+c?

Also, how do you characterize the relationship between two rectangles such as in the examples above? I want to say something like "n(n+c) and a(a+c) are two rectangles of the same proportion," but I'm not sure that's the right word.

Thanks!

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