We address the problem of determining what points in a field satisfy Freshman's Dream, or equivalently, when a monomial behaves additively. It is conjectured that the only additive points over the rational numbers are trivial. In the case of finite fields, we generalize well-known results about uni-variate polynomials to bivariate homogeneous polynomials in order to count the number of additive points.
Abramson, Michael P.
"When is Freshman's Dream Actually True?,"
The Mathematics Enthusiast: Vol. 18
, Article 2.
Available at: https://scholarworks.umt.edu/tme/vol18/iss1/2