How do you make a pythagorean triple?

Answer 1

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.