Pythagorean theorem states that:
c^2=a^2+b^2
where:
c=hypotenuse
a and b are the legs
this implies that, a and b are shorter than c; thus to find the Pythagorean theorem we look for values that satisfy the above equation, where c is the longest side.
17^2=15^2+9^2
thus (17,15,9) are Pythagorean triple.
13^2=5^2+12^2
Thus (5,12,13) are Pythagorean triple
12^2≠6^2+8^2
Thus they are not Pythagorean triple
6^2=5^2+3^2
Thus (3,5,6) are not Pythagorean theorem.