Question 1.4: maximum multiplicity with distinct moduli

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Updated Oct 7

Source. Question 1.4, printed p. 1740, physical PDF p. 2.

Statement

Harrington asks (p. 1740): "What is the largest positive integer $N$ such that every integer satisfies at least $N$ congruences of a covering system with distinct moduli greater than 1?"

The source takes Sun's definition (Definition 1.5): a system in which every integer satisfies at least $m$ congruences is an $m$ -covering; that definition by itself does not require distinct moduli.

Source result. The paper's Section 4 construction shows $N\geq3$ . It does not determine the largest $N$ .

Bears on. This question is motivated by the bounded minimum modulus in Problem 2, but it is a different extremal parameter.

Linked from (3)

Problem 2 Two Questions Concerning Covering Systems Section 4: a three-cover with distinct moduli

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