  Given an equation, the integers $[n] = \{1, 2, \dots, n\}$ as inputs, and the
colors red and blue, how can we color $[n]$ in order to minimize the number of
monochromatic solutions to the equation, and what is the minimum? The answer is
only known for a handful of equations, but much progress has been made on
improving upper and lower bounds on minima for various equations. A
well-studied characteristic an equation, which has its roots in graph Ramsey
theory, is to determine if the minimum number of monochromatic solutions can be
achieved (asymptotically) by uniformly random colorings. Such equations are
called common. We prove that no 3-term equations are common and provide a lower
bound for a specific class of 3-term equations.
