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Counterexamples to a Conjecture of Dombi in Additive Number Theory
- Publication Year :
- 2022
-
Abstract
- We disprove a 2002 conjecture of Dombi from additive number theory. More precisely, we find examples of sets $A \subset \mathbb{N}$ with the property that $\mathbb{N} \setminus A$ is infinite, but the sequence $n \rightarrow |\{ (a,b,c) \, : \, n=a+b+c \text{ and } a,b,c \in A \}|$, counting the number of $3$-compositions using elements of $A$ only, is strictly increasing.<br />Comment: additional author added; largely rewritten with different example
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2212.12473
- Document Type :
- Working Paper