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?(adsbygoogle = window.adsbygoogle || []).push({});

1) Given that n^{2}-a^{2}= (n-a)(n+a), it follows that (n^{2}+cn)-(a^{2}+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!

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Congruence of rectangles? please help

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

Loading...

Similar Threads - Congruence rectangles please | Date |
---|---|

I Congruence Subgroups and Modular Forms Concept Questions | Dec 27, 2016 |

Basic Congruences Confusion | Nov 12, 2012 |

A Theorem on Squares and Congruences | Oct 21, 2012 |

Residues and non residues of general quadratic congruences | Oct 12, 2012 |

3D Transformation of Rectangle to a Plane | Mar 31, 2012 |

**Physics Forums - The Fusion of Science and Community**