Additivity — Sums of Powers

This chapter is dedicated to additivity in number theory. In particular, the problem of representing integers as a sum of squares goes back to Diophantus, who ostensibly knew that every n ∈ N is a sum of at most four integer squares of positive numbers — see Biography 1.15 on page 48. Later, Fermat, then Euler, and more substantially Lagrange made contributions to the representation problem. We begin with the simplest of the additive representations.