Sidon sets from Erdős and Turán to yesterday

Abstract

Motivated by some problems in Fourier analysis, Sidon asked for the maximum number of integers in a block of given length with the property that their pairwise sums are all distinct. The first estimate is due to P. Erdős and P. Turán [J. Lond. Math. Soc. (1) 16 (1941), 212–215]. This started the theory of what came to be called “Sidon sets.” We present some classical gems and a couple of recent developments.