On a Theorem of J. E. Olson and an Application (Vanishing Sums in Finite Abelianp-Groups)

AbstractGeneralizing a theorem by J. E. Olson determining the Davenport's constant of a finite abelianp-groupA, we prove that ifS1, ...,Skare given sets of integers satisfying suitable conditions and ifg1, ...,gk∈A, then a nontrivial vanishing sum of the forms1g1+ ··· +skgk,si∈Simay be found. The result may be applied to the problem of finding polynomials inFp[x] having small degree and prescribed value set onFp