Refined Estimates Concerning Sumsets Contained in the Roots of Unity

Abstract

We prove that the clique number of the Paley graph is at most $\sqrt{p/2}+1$, and that any supposed additive decompositions of the set of quadratic residues can only come from co-Sidon sets.

7 pages. The second version already included a corollary to Theorem 1.2 due to George Shakan that confirms Sarkozy's conjecture for almost all primes