Golomb's conjectures and related problems
The conjectures of \textit{S. Golomb} [J. Comb. Theory, Ser. A 37, 13-21 (1984; Zbl 0547.05020)]\ concern the representability of elements of a finite field as sums of two primitive elements. Using tools from analytic number theory, the author obtains an asymptotic formula for the number of such representations in the special case of finite fields \(GF(p)\), \(p\) an odd prime. As a corollary, the Golomb conjectures hold in \(GF(p)\) if \(p-1\) does not have too many prime divisors.
scientific article; zbMATH DE number 817773