Steven Post of Edgewood college. 32 + 42 = 52 : Now What? When student first learn the Pythagorean Theorem relating the sides of a right triangle one of the first triangles they meet is the 3 – 4 – 5 triangle. But in general most right triangles don’t have side lengths which are all integers. In this talk we see how to find more such triangles – in fact all of them – using geometry. We then generalize that approach to another interesting class of equations which turns out to have very deep applications in advanced number theory (including cryptography!) Questions? Contact John Grade at JDGrade@madisoncollege.edu (608) 246-6712