When only the empty subsum is zero modulo \(p\). (Quand seule la sous-somme vide est nulle modulo \(p\).) (French) Zbl 1153.11007

A famous conjecture of Selfridge implies that any set \(S\) of residue classes modulo a prime \(p\) having no nonempty subset summing to zero must satisfy the condition \(|S|\leq\sqrt{2p}\). The author obtains an asymptotic solution for the last question using analytical tools.


11B34 Representation functions
11P70 Inverse problems of additive number theory, including sumsets
11B50 Sequences (mod \(m\))
20D60 Arithmetic and combinatorial problems involving abstract finite groups


zero-sum subset
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