F. J. M. Barning gave a matrix-based generation process for primitive Pythagorean triples. His 1963 Mathematisch Centrum report verifies the initials and presents three unimodular matrices generating all such triples without repetition, with a fixed leg-order convention.[ref]
The transformations preserve the equation . Starting from , with the even leg first, repeated transformations build a branching tree of solutions. The method turns a Diophantine equation into a recursive enumeration algorithm with a uniqueness theorem.[ref]
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