how many primitive Pythagorean triples are there up to 100?

Question

how many primitive Pythagorean triples are there up to 100?

Answer 1

There are 16 of them, according to Wikipedia:

A Pythagorean triple consists of three positive integers a, b, and c, such that a² + b² = c². Such a triple is commonly written (a, b, c), and a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k. A primitive Pythagorean triple is one in which a, b and c are coprime.

The name is derived from the Pythagorean theorem, of which every Pythagorean triple is a solution. The converse is not true. For instance, the triangle with sides a = b = 1 and c = √2 is right, but (1, 1, √2) is not a Pythagorean triple because √2 is not an integer. Moreover, 1 and √2 don't have an integer common multiple because √2 is irrational. There are 16 primitive Pythagorean triples with c ≤ 100:
( 3, 4, 5) ( 5, 12, 13) ( 7, 24, 25) ( 8, 15, 17)
( 9, 40, 41) (11, 60, 61) (12, 35, 37) (13, 84, 85)
(16, 63, 65) (20, 21, 29) (28, 45, 53) (33, 56, 65)
(36, 77, 85) (39, 80, 89) (48, 55, 73) (65, 72, 97)

Answer 2

Primitive Pythagorean Triples List

Answer 3

There are 16 primitive Pythagorean triples with c ≤ 100:

( 3, 4, 5) ( 5, 12, 13) ( 7, 24, 25) ( 8, 15, 17)
( 9, 40, 41) (11, 60, 61) (12, 35, 37) (13, 84, 85)
(16, 63, 65) (20, 21, 29) (28, 45, 53) (33, 56, 65)
(36, 77, 85) (39, 80, 89) (48, 55, 73) (65, 72, 97)

Answer 4

This Site Might Help You.

RE:
how many primitive Pythagorean triples are there up to 100?
how many primitive Pythagorean triples are there up to 100?

Answer 5

Check this site.

http://www.mcs.surrey.ac.uk/Personal/R.Knott/Pythag/pythag.html

They have a list of Pythagorean triples up to 100 about a quarter down the page.

Answer 6

yeah, pretty much what is above me