Dummit and Foote has a fun way of classifying Pythagorean triples. It is a classic fact that if $(a, b, c)$ is a reduced Pythagorean triple then there exists integers $m, n$ such that $$ \begin{align*} a &= m^2 - n^2, \ b &= 2mn, \ c &= m^2 + n^2. \end{align*} $$ To prov . . . Read more