Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:defines |
A set of three positive integers a, b, c such that a^2 + b^2 = c^2
|
| gptkbp:example |
(3, 4, 5)
(5, 12, 13) (8, 15, 17) |
| gptkbp:form |
a = m^2 - n^2, b = 2mn, c = m^2 + n^2 for integers m > n > 0
|
| https://www.w3.org/2000/01/rdf-schema#label |
Pythagorean triple
|
| gptkbp:property |
Exactly one of a or b is divisible by 3 in primitive triples
One of a or b is even, the other is odd in primitive triples Primitive Pythagorean triples have a, b, c coprime There are infinitely many Pythagorean triples Exactly one of a, b, c is divisible by 5 in primitive triples a and b are the legs of a right triangle Exactly one of a or b is divisible by 4 in primitive triples c is always odd in primitive triples c is the hypotenuse in a right triangle a, b, c are coprime in a primitive Pythagorean triple All multiples of a Pythagorean triple are also Pythagorean triples |
| gptkbp:relatedTo |
gptkb:Pythagorean_theorem
|
| gptkbp:usedIn |
gptkb:geometry
number theory |
| gptkbp:bfsParent |
gptkb:Pythagorean_theorem
|
| gptkbp:bfsLayer |
5
|