Fermat's Last Theorem and Pythagorean Triples

Fermat's Last Theorem is investigated on the set of Pythagorean triples using the ancient Greek formulas of Pythagoras, Euclid, and Plato. These are formulas used to derive natural number solutions of the Pythagorean theorem. Since Euclid’s formula makes all possible triples, proofs that Euclid’s cannot work at higher powers thus prove Fermat’s on the set of triples.