Three natural numbers (a,b,c) are called a "Pythagorean triple" if a2 + b2 = c2
Note: calculations using the Pythgoras lemma in most cases result in answers with roots.
The most well-known Pythagorean triple is (3,4,5) because 32 + 42 = 52
Question: are there more triples?
b2 = c2 - a2
b2 = (c - a)(c + a)
c + a = y2.............so
b2 = x2y2
b = xy
The original formula a2 + b2 = c2 may be rewritten as:
b = 2 x y
c = y 2 + x 2
There exists an infinite number of Pythagorean triples.
Some triples are not very original as they are just multiples of earlier triples.
Basic triples have no common factors or: GCD(a,b) = 1
A small Delphi program calculates the triples:
download program (zip format)
download Delphi-7 project