Let m and n be an integer and m > n. You can generate triples with:
a = 2mn
b = m^2 - n^2
c = m^2 + n^2
For example, let m = 4 and n = 3.
a = 2(3)(4) = 24
b = 4^2 - 3^2 = 7
c = 4^2 + 3^2 = 25
Therefore, you'd have the triple (24, 7, 25).
Check:
24^2 + 7^2 = 25^2
==> 576 + 49 = 625
==> 625 = 625
This set is a Pythagorean triple.
Another, example, let m = 2 and n = 1.
a = 2(2)(1) = 4
b = 2^2 - 1^2 = 3
c = 2^2 + 1^2 = 5
We got a very common set of a Pythagorean Triples this time!
Hope this helps!
