1. The problem statement, all variables and given/known data Show that the curve x^3+3xy+y^3=1 contains only one set of three distinct points A,B, and C, which are vertices of an equilateral triangle. 2. Relevant equations 3. The attempt at a solution I randomly starting plotting points and found that all of them fell on the line y=1-x except (-1,-1). So, I just need to prove that these are the only points that satisfy that equation. It turns out that that equation factors into a very useful form. See B1 http://www.unl.edu/amc/a-activities/a7-problems/putnam/-pdf/2006s.pdf My question is how would you "discover" that really nice form if you were taking the test?