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OPEN This is open, and cannot be resolved with a finite computation.
Is there a covering system all of whose moduli are of the form $p-1$ for some primes $p\geq 5$?
Disclaimer: The open status of this problem reflects the current belief of the owner of this website. There may be literature on this problem that I am unaware of, which may partially or completely solve the stated problem. Please do your own literature search before expending significant effort on solving this problem. If you find any relevant literature not mentioned here, please add this in a comment.
Selfridge has found an example using divisors of $360$ if $p=3$ is allowed.

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This page was last edited 01 October 2025.

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When referring to this problem, please use the original sources of Erdős. If you wish to acknowledge this website, the recommended citation format is:

T. F. Bloom, Erdős Problem #273, https://www.erdosproblems.com/273, accessed 2026-01-16