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A note on a problem of Ma and Chen
Abstract
Let S=(s1,s2,⋯) be a strictly increasing sequence of positive integers. For any real number α>0, let Sα=(⌊αs1⌋,⌊αs2⌋,⋯). We prove that if sn+1≤ 2sn for every positive integer n, then there exists 0<α<1 such that Sα is strongly complete. In addition, this gives a negative answer to a problem of Ma and Chen in [Acta Arith. 203 (2022), 307--318]. We also prove that the same result is true if sn+1≤ 2sn for all sufficiently large n.
Related
BibTeX
@misc{wu2026note,
title = {{A note on a problem of Ma and Chen}},
author = {Bing-Ling Wu and Wu-Xia Ma},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38288},
eprint = {2610.38288},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38288},
}
RIS
TY - UNPB
TI - A note on a problem of Ma and Chen
AU - Bing-Ling Wu
AU - Wu-Xia Ma
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38288
UR - https://arxiv.org/abs/2610.38288
AB - Let S=(s_1,s_2,⋯) be a strictly increasing sequence of positive integers. For any real number α>0, let S_α=(⌊αs_1⌋,⌊αs_2⌋,⋯). We prove that if s_n+1≤ 2s_n for every positive integer n, then there exists 0<α<1 such that S_α is strongly complete. In addition, this gives a negative answer to a problem of Ma and Chen in [Acta Arith. 203 (2022), 307--318]. We also prove that the same result is true if s_n+1≤ 2s_n for all sufficiently large n.
ER -