# Book describes some Pythagorean triples as uninteresting, favoring “primitive” Pythagorean triples. Why?

Background

Chapter 2 starts with discussing Pythagorean triples (PT), which is an ordered triple $(a, b, c)$ such that $a^2 + b^2 = c^2$.

It further shows the existence of an infinite number of such triples, by showing that given $a^2 + b^2 = c^2$ and some $d\in\mathbb N$, then $(da, db, dc)$ is another PT, and shows a simple proof.

Then it states:

Clearly these new Pythagorean triples are not very interesting. So we will concentrate our attention on triples with no common factors. Primitive Pythagorean triples (PPT).

Question

Why are PPTs more interesting? I understand that these are going to be rarer, but do they have some sort of application that regular PTs don't have?

• The "new" Pythagorean triples are uninteresting in the sense that once you know everything about primitive triples you know everything about the "new' triples. So it is more productive to put the primitive constraint on the triples and study only those. – Malcolm Dec 17 '17 at 13:56
• @Malcolm - That's a good point. – Alec Dec 17 '17 at 14:07