Resumen de Condiciones algebraicas de existencia de Ternas Pitagóricas

Jesús Álvarez Mesa

• It is known that the equation x² + y² = z² has infinite solutions in positive whole numbers, in the same way as ^x² + ŷ² = 1, with ^x = x/z, ŷ = y/z, has infinite rational positive solutions. This article proves that rational solutions of ^x² + ŷ² = 1 can only be achieved if the quotient ^x/ŷ fulfils specific algebraic conditions that are investigated and, consecuently, we can oly obtain Pythagorean triples (x,y,z) if those conditions are confirmed. Finally, Pythagorean triples are obtained from the equations that have been used previously.