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Note on a Result of Haddad and Helou
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Chi-Wu Tang
Published/Copyright:
May 31, 2010
Abstract
Let K be a field of characteristic ≠ 2 and G the additive group of K × K. In 2004, Haddad and Helou constructed an additive basis B of G for which the number of representations of g ∈ G as a sum b1 + b2(b1, b2 ∈ B) is bounded by 18. In this paper, we proceed to investigate the parallel problem for differences.
Received: 2009-06-31
Revised: 2010-01-18
Accepted: 2010-01-23
Published Online: 2010-05-31
Published in Print: 2010-May
© de Gruyter 2010
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Articles in the same Issue
- Recounting the Number of Rises, Levels, and Descents in Finite Set Partitions
- Multiplicities of Integer Arrays
- Adjugates of Diophantine Quadruples
- A Binary Tree Representation for the 2-Adic Valuation of a Sequence Arising From a Rational Integral
- On a Variant of Van Der Waerden's Theorem
- Note on a Result of Haddad and Helou
- Sequences of Density ζ(k) – 1
- Square-Full Divisors of Square-Full Integers
- Lower Bounds for the Principal Genus of Definite Binary Quadratic Forms
