bibkey: bispels2025oddcovering authors: “Chris Bispels; Matthew Cohen; Joshua Harrington; Joshua Lowrance; Kaelyn Pontes; Leif Schaumann; Tony W. H. Wong” year: 2025 title: “A further investigation on covering systems with odd moduli” doi: 10.1016/j.disc.2026.115013 url: https://arxiv.org/abs/2507.16135 claim: “The unrestricted distinct odd covering problem is still described as open; the paper studies the variant in which one odd modulus may repeat while all other odd moduli remain distinct.” strata_touched:
- D5/S3/Arith/Congruence/TwoOddPrimeUncoveredDensity license: citation-only triage: anchor
A further investigation on covering systems with odd moduli
The inspected source is arXiv:2507.16135, submitted 22 July 2025 (manuscript dated 3 September 2025). Crossref records the published version as Discrete Mathematics 349 (2026), article 115013, DOI 10.1016/j.disc.2026.115013.
The abstract explicitly distinguishes the original Erdos odd-covering problem
from the variant studied in the paper: one odd modulus may be used repeatedly,
while every other modulus is a distinct odd integer greater than one. The paper
gives upper bounds for the permitted multiplicity in that variant, including
Theorem 2.4 (t_p <= p-5 for primes p >= 17). These are construction
results for the repeated-modulus variant. They neither produce a cover with
all moduli distinct nor prove nonexistence of such a cover.
This citation therefore updates the literature boundary only. It supplies no new proof obligation or unrestricted Erdos–Selfridge #7 settlement.