Frequently Asked Questions
What is a Pythagorean triple?
Three positive integers a, b, c with a squared plus b squared equals c squared. The triple is primitive if a, b, c have no common factor greater than 1.
How do I find primitive triples?
Use Euclid's formula with m greater than n, both positive integers, with greatest common divisor one and opposite parity. Every primitive Pythagorean triple arises this way exactly once.
Why does Euclid's formula work?
Because (m squared minus n squared) squared plus (2 m n) squared equals (m squared plus n squared) squared is a polynomial identity, derived from the factorization of c squared minus a squared.
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