An addition theorem modulo \(p\). (English) Zbl 0174.05202

Author’s summary: Let \(a_1,\ldots, a_s\) be distinct non-zero residue classes modulo a prime \(p\). In this paper we estimate the number of residue classes represented by \(\varepsilon_1a_1+\ldots+\varepsilon_sa_s\) where the \(\varepsilon_i\) are restricted to the values 0 and 1. In particular, we verify a conjecture of P. Erdős and H. Heilbronn [Acta Arith. 9, 149–159 (1964; Zbl 0156.04801)]: every residue class is represented if \(s>2p^{1/2}\).
Reviewer: H. B. Mann


11A07 Congruences; primitive roots; residue systems
11B13 Additive bases, including sumsets


Zbl 0156.04801
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