the set of integers {3,4,5} is a pythagorean triple. another such sets is?

Answer 1

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

Another such set is 5,12,13.
Here is a table of infinitely many such triples:
3 4 5
5 12 13
7 24 25
9 40 41
11 60 61
13 84 85
We can continue this pattern and
find a Pythagorean triple whose
smallest member is any odd
number greater than or equal to 3.