Problem 7 — Visual explainer (undergrad)
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Problem statement
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Is there a distinct covering system all of whose moduli are odd?

Picture
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[Given objects + constraints]  --->  [Count / structure]  --->  [Show bound / existence]

Question: what to look at
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- Restate the problem as: given the constraint, what asymptotic bound or
  structure must follow?
- Use the comments as benchmarks (best known bounds / constructions).

Benchmarks / known results (from comments)
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- The answer to this stronger question is no, proved by Balister,
  Bollob\'{a}s, Morris, Sahasrabudhe, and Tiba.
- Hough and Nielsen proved that at least one modulus must be divisible by
  either $2$ or $3$.
- A simpler proof of this fact was provided by Balister, Bollob\'{a}s, Morris,
  Sahasrabudhe, and Tiba, who also prove that if an odd covering system exists
  then the least common multiple of its moduli must be divisible by $9$ or
  $15$.
- Selfridge has shown (as reported in ) that such a covering system exists if
  a covering system exists with moduli $n_1,\ldots,n_k$ such that no $n_i$
  divides any other $n_j$ (but the latter has been shown not to exist, see
  [586]).