Difference between revisions of "Pythagorean triple"
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== Primitive Pythagorean Triples == | == Primitive Pythagorean Triples == | ||
| − | A Pythagorean Triple is primitive if it has no common factors. | + | A Pythagorean Triple is primitive if it has no common factors, so that they are [[relatively prime]]. All of the above are primitive. Multiples of the above triples will also satisfy <math>a^2 + b^2 = c^2</math>; for example, any three numbers in the form of <math>(3x, 4x, 5x)</math>, like <math>(6, 8, 10)</math>, will also satisfy it. |
| − | == See | + | == See also == |
* [[Pythagorean Theorem]] | * [[Pythagorean Theorem]] | ||
* [[Diophantine equation]] | * [[Diophantine equation]] | ||
Revision as of 16:17, 28 February 2007
A Pythagorean Triple is a triple of positive integers, 
such that 
. Pythagorean Triples arise in geometry, as the side-lengths of right triangles.
Common Pythagorean Triples
These are some common Pythagorean Triples:
(3, 4, 5)
(20, 21, 29)
(11, 60, 61)
(13, 84, 85)
(5, 12, 13)
(12, 35, 37)
(16, 63, 65)
(36, 77, 85)
(8, 15, 17)
(9, 40, 41)
(33, 56, 65)
(39, 80, 89)
(7, 24, 25)
(28, 45, 53)
(48, 55, 73)
(65, 72, 97)
Primitive Pythagorean Triples
A Pythagorean Triple is primitive if it has no common factors, so that they are relatively prime. All of the above are primitive. Multiples of the above triples will also satisfy ; for example, any three numbers in the form of 
, like 
, will also satisfy it.
