Open Problem 1: arbitrarily large minimum modulus

Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.

Updated Oct 8

Source. Open Problem 1, printed p. 1 (PDF p. 2) of the 22 May 2001 author manuscript.

Statement

For every $c>0$ , does there exist a finite covering of the integers with distinct moduli and minimum modulus at least $c$ ?

Bears on. This is the question of Problem 2 in its corrected form (distinct moduli), asked for every bound $c$ . The question is transcribed here in its 2001 form; the manuscript answers no part of it, and it notes (p. 1) Morikawa's announced covering with $c=24$ .

Linked from (2)

Problem 2 On Coverings of the Integers Associated with an Irreducibility Theorem of A. Schinzel

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