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Large Zero-Free Subsets of ℤ/pℤ
-
Jean-Marc Deshouillers
and
Gyan Prakash
Published/Copyright:
June 4, 2011
Abstract
A finite subset 
of an abelian group 
is said to be zero-free if the identity element of cannot be written as a sum of distinct elements from . In this article we study the structure of zero-free subsets of ℤ/pℤ, the cardinalities of which are close to the largest possible. In particular, we determine the cardinality of the largest zero-free subset of ℤ/pℤ, when p is a sufficiently large prime.
Keywords.: Inverse Additive Problems; Zero-Free Sets
Received: 2009-01-23
Revised: 2010-07-07
Accepted: 2010-09-08
Published Online: 2011-06-04
Published in Print: 2011-June
© de Gruyter 2011
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Articles in the same Issue
- Preface
- On the Intersections of Fibonacci, Pell, and Lucas Numbers
- Proving Balanced T2 and Q2 Identities Using Modular Forms
- Sum-Product Inequalities with Perturbation
- Power Totients with Almost Primes
- On the Sum of Reciprocals of Amicable Numbers
- Tromping Games: Tiling with Trominoes
- There are No Multiply-Perfect Fibonacci Numbers
- Large Zero-Free Subsets of ℤ/pℤ
Articles in the same Issue
- Preface
- On the Intersections of Fibonacci, Pell, and Lucas Numbers
- Proving Balanced T2 and Q2 Identities Using Modular Forms
- Sum-Product Inequalities with Perturbation
- Power Totients with Almost Primes
- On the Sum of Reciprocals of Amicable Numbers
- Tromping Games: Tiling with Trominoes
- There are No Multiply-Perfect Fibonacci Numbers
- Large Zero-Free Subsets of ℤ/pℤ
