Towards 3n - 4 in groups of prime order
We show that if A is a subset of a group of prime order p such that |2.Al < 2.7652|Al and 10 < |A| < 1.25 - 10-®p, then A is contained in an arithmetic progression with at most 2A - [Al + 1 terms, and 2.4 contains an arithmetic progression with the same difference and at least 2|A - 1 terms...
| Authors: | , |
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| Format: | article |
| Publication Date: | 2023 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/392259 |
| Online Access: | https://hdl.handle.net/2117/392259 https://dx.doi.org/10.37236/11976 |
| Access Level: | Open access |
| Keyword: | Sequences (Mathematics) Partitions (Mathematics) Successions (Matemàtica) Particions (Matemàtica) Classificació AMS::11 Number theory::11B Sequences and sets Classificació AMS::11 Number theory::11P Additive number theory partitions Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres |
| Summary: | We show that if A is a subset of a group of prime order p such that |2.Al < 2.7652|Al and 10 < |A| < 1.25 - 10-®p, then A is contained in an arithmetic progression with at most 2A - [Al + 1 terms, and 2.4 contains an arithmetic progression with the same difference and at least 2|A - 1 terms. This improves a number of previously known results. |
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