Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
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Claim. Michael Schroeder's Noncoverage for Distinct Odd Moduli with at Most Three Prime Divisors asserts that a finite family of residue classes with distinct odd moduli greater than one cannot cover all integers if every individual modulus has at most three distinct prime divisors.
Covers. The negative answer to Problem 7 under this restriction on each modulus. Prime powers and the total number of primes across the family are unrestricted. The conclusion is distinct from bounding the prime support of the overall least common multiple; neither restriction treats all possible odd covers.
Standing. Claimed. The author's research-page description, dated 2026-09-09 and revised 2026-09-15, and the forum announcement were read on 2026-10-16. They report a Lean proof. The manuscript, proof and supporting formalization were not checked here, and no independent review or journal acceptance was located in those records.
Depends on. Nothing in this wiki. The announced proof uses a system of factorial moments; its hypotheses and implementation have not been audited.
Submission note. The author posted the result to the problem's discussion on 2026-09-15.