Geodesic
Covering Classes of Residues
Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 514-519

Voir la notice de l'article provenant de la source Cambridge University Press

A set of ordered pairs of integers {(ai, mi)} is said to cover the integers if each integer x satisfies the congruence x ≡ ai (mod mi ) for some i. We may assume that the mi are positive. Trivially {(0, 1)} covers, as does {(0, m), (1, m), (2, m), ... , (m — 1, m)}. In order to arrive at some non-trivial problems concerning covers, the following definition is given: A finite set of ordered pairs of integers with mi > 1 andmi ≠ mj if i ≠ j, is called a covering class of residues if every integer x satisfies the congruence x ≡ ai (mod mi) for some i. 
Jordan, James H. Covering Classes of Residues. Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 514-519. doi: 10.4153/CJM-1967-043-0
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