Solution of the minimum modulus problem for covering systems
Bob Hough
TL;DR
This paper proves that the smallest modulus in any distinct covering system of congruences cannot exceed 10^{18}, resolving a question posed by Erdős.
Contribution
It establishes an explicit upper bound on the minimum modulus for covering systems, advancing understanding of their structure.
Findings
Least modulus is at most 10^{18} for covering systems
Answers Erdős's longstanding question
Provides bounds relevant to number theory and combinatorics
Abstract
We answer a question of Erd\H{o}s by showing that the least modulus of a distinct covering system of congruences is no larger than .
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