Assertion: heronian triangle | /r/HasAspect | side
Facets:
value: k
type: OTHER
Source sentences:
text: Heronian triangles that have no integer altitude (indecomposable and non-Pythagorean) have sides that are all divisible by primes of the form 4 k +1.  
text: However decomposable Heronian triangles must have two sides that are the hypotenuse of Pythagorean triangles.
text: Therefore, all Heronian triangles have at least one side that is divisible by primes of the form 4 k +1.
text: Hence all Heronian triangles that are not Pythagorean have at least two sides that are divisible by primes of the form 4 k +1.
text: The Indian mathematician Brahmagupta (598-668 A.D.) derived the parametric solution such that every Heronian triangle has sides proportional to:
text: Every Heronian triangle has sides proportional to
text: However decomposable Heronian triangles must have two sides that are the hypotenuse of Pythagorean triangles.
text: Therefore, all Heronian triangles have at least one side that is divisible by primes of the form 4 +1.
text: Hence all Heronian triangles that are not Pythagorean have at least two sides that are divisible by primes of the form 4 +1.