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Old and new necessary and sufficient conditions on \((a_i, m_i)\) in order that \(n\equiv a_i \pmod{m_i}\) be a covering system. (English) Zbl 1071.11012
A covering system is a set of congruences \(n\equiv a_1 ({\operatorname {mod}}\,\, m_i), \, i=1,\dots ,k,\) such that every integer satisfies at least one of them. A new necessary and sufficient condition in order that a given set of congruences \(n\equiv a_1 ({\operatorname {mod}}\,\, m_i)\) be a covering system is established and its correlations to known conditions are studied.

MSC:
11B25 Arithmetic progressions
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References:
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