Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 8 min ago
PreprintCC BY 4.0arXiv

On additive complements in natural numbers

  • Quan-Hui Yang
  • Lilu Zhao
Open at sourcePDFDOICite

Abstract

We prove that for additive complements A and B, if limsupx→+∞A(x)B(x)/x<4/3, then A(x)B(x)−x→+∞ (x→+∞). This improves the earlier upper bound 3−√3 due to Fang and Chen.

Related

  1. A Sharp Bound for Additive Complements
    Zihan Zhang
    arXivPreprintCC BY-NC-SA 4.0Full textAlgebra & number theoryarXiv
  2. On almost perfect additive complements
    Wouter van Doorn, Boning Liu, Quanyu Tang
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  3. On a problem of Ma and Chen concerning minimal additive complements
    Shi-Qiang Chen, Quan-Hui Yang
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsarXiv
  4. A lower bound for additive complements to the primes
    Artyom Radomskii
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  5. The law of large numbers for non-additive capacities without continuity
    Li-Xin Zhang
    arXivPreprintarXiv licenceFull textProbabilityarXiv

Cite

BibTeXRIS
BibTeX
@misc{yang2026additive,
  title = {{On additive complements in natural numbers}},
  author = {Quan-Hui Yang and Lilu Zhao},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.13900},
  eprint = {2609.13900},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.13900},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On additive complements in natural numbers
AU  - Quan-Hui Yang
AU  - Lilu Zhao
PY  - 2026
DA  - 2026/09/12
PB  - arXiv
DO  - 10.48550/arxiv.2609.13900
UR  - https://arxiv.org/abs/2609.13900
AB  - We prove that for additive complements A and B, if limsup_x→+∞A(x)B(x)/x<4/3, then A(x)B(x)−x→+∞ (x→+∞). This improves the earlier upper bound 3−√3 due to Fang and Chen.
ER  -