Suppose we manage to find a solution to an equation. Is it the “simplest” solution we could have found? For example, we might note that x = 374 is a solution to x^3 - 587x^2 + 80084x - 157828, but if we think even less hard about it, so is x = 2. Sometimes "small" is what we mean by “simple,” but sometimes we need of notion of “simple” with a little more oomph. (Are 1/7 or sqrt(2)-1 simpler than 1? They're smaller!) In this talk, we'll see some of analytic number theory's tools for finding “simple” solutions to Diophantine equations.
Nick Rauh is a mathematics faculty member at Sarah Lawrence College. BS, Harvey Mudd College. PhD, University of Texas. Areas of expertise include number theory and recreational mathematics. Former chief of mathematics, National Museum of Mathematics. Previously taught at University of Texas and Texas State University.