What are these sets of Pythagorean triples called?

Question

There are sets of Pythagorean triples $$ \{ a, b, c\} $$ where any pair of numbers is relative prime, like {3, 4, 5} and {5, 12, 13}, and there are sets with common factors $$ \{ n \cdot a, n \cdot b, n \cdot c \} $$ like the obvious {6, 8, 10} or {30, 40, 50}. What are both sets called?

http://en.wikipedia.org/wiki/Tree_of_primitive_Pythagorean_triples — lab bhattacharjee, Jan 11 '14 at 11:16
"Primitive Pythagorean triples" and "Non-primitive Pythagorean triples". — Daniel Fischer, Jan 11 '14 at 11:16

MJD · Accepted Answer · 2014-01-22T15:25:58.493

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As Daniel Fischer says in a comment, a pythagorean triple $(a,b,c)$ where $\gcd(a,b,c) = 1$ is usually called a primitive pythagorean triple. The antonym is "non-primitive".

edited Jan 22 '14 at 15:25

answered Jan 20 '14 at 18:09

MJD

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score 0 · Answer 2 · answered Jan 20 '14 at 18:13

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The ones who have not common factors are called primitive pythagorean triplets, the ones who have non-primitive pythagorean triplets.

BYE!

answered Jan 20 '14 at 18:13

PunkZebra

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What are these sets of Pythagorean triples called?

2 Answers2