A study of Pythagorean triples

This paper explores various aspects of the integral solutions to the Pythagorean equation, $x\sp2+y\sp2=z\sp2$. These solutions are known as Pythagorean Triples. Solutions where all three variables are relatively prime, known as Primitive Pythagorean Triples, are studied in detail. Several methods of generating these solutions are discussed. An application to geometry is explored. Then, the material regarding Primitive Pythagorean Triples is reviewed in terms of solutions to the similar equation, $x\sp2+y\sp2=z\sp2+k$.