Prerequisites for Pythagorean Triples

This research problem is a good starting investigation for any middle or high school student.  The most fundamental prerequisite is a knowledge of Pythagoras’ Theorem.  In addition, some familiarity with properties of integers, such as divisibility and parity (odd/even), would be helpful (see Number Theory).  Many questions might come to mind immediately.  If you run out of ideas, you might want to consult the Problem Posing discussion.

The mathematical topics that are familiar to you will influence the types of questions you ask. However, if you do not have the mathematical knowledge needed to answer one of the questions, ask your teacher or mentor what you would need to learn and if you are ready to study that new topic.

Knowing about modular arithmetic may help you prove some of your conjectures.