A Pythagorean triple is a set of three integers which form the sides of a right trianle.
We can test the triples by plugging them into the Pythagorean theorem.
the Pythagorean theorem is c=√a²+b²
5=√(3)²+(4)²
5=√9 + 16
5=√25
5=5
so we can prove the 3,4,and 5 is in fact a Pythagorean triple.
17=√(8)²+(15)²
17=√64+225
17=√289
17=17
so we can prove that 8,15,and 17 is also a Pythagorean triple.