Noun
Pythagorean triple (plural Pythagorean triples)
(mathematics) A set of three positive integers a, b and c, for which
a
2
+
b
2
=
c
2
{\displaystyle a^{2}+b^{2}=c^{2}}
As it is only a necessary condition but not a sufficient one, it can be used in checking if a given triple of numbers is not a Pythagorean triple when they fail the test. Source: Internet
The two factors and of a primitive Pythagorean triple each equal the square of a Gaussian integer. Source: Internet
Conversely, any point on the unit circle whose coordinates x, y are rational numbers gives rise to a primitive Pythagorean triple. Source: Internet
The Heronian triple (a, b, c) is primitive provided a, b, c are pairwise relatively prime (as with a Pythagorean triple). Source: Internet
There are 16 primitive Pythagorean triples with c ≤ 100 : Note, for example, that (6, 8, 10) is not a primitive Pythagorean triple, as it is a multiple of (3, 4, 5). Source: Internet
Thus, the first factor can be written : The real and imaginary parts of this equation give the two formulas: : For any primitive Pythagorean triple, there must be integers m and n such that these two equations are satisfied. Source: Internet