Use Euclid's formula.
Take any two integers m and n that are coprime and let m > n
(if not, just swap them around).
Then
a = m2 - n2
b = 2mn
and
c = m2 + n2
form a primitive Pythogorean triple.
And since (a, b, c) is a Pythagorean triple then so is (k*a,
k*b, k*c) for any integer k, except that the latter is not
primitive.