A triple (a, b, c) of integers that satisfies the equations
a2 + b2 = c2
is called a Pythagoras’ triple. There are infinitely many such triples.
For example, (3, 4, 5), (5, 12, 13), (8, 15, 17) are Pythagoras’ triples.
Here is one method (Euler) for generating Pythagoras’ triples:
For any positive integers m > n, let
a = m2 − n2
b = 2mn
c = m2 + n2
Then (a, b, c) is a Pythagoras’s triple.
For example, if n = 1 and m = 2 then
a = 3, b = 4, c = 5 and
32 + 42 = 52
On the website http://www.cut-the-knot.org/pythagoras/pythTriple.shtml Alexander Bogomolny provides an applet that generates all Pythagorasís triples.