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Covering Classes of Residues

Published online by Cambridge University Press:  20 November 2018

James H. Jordan
James H. Jordan*
Affiliation:
Washington State University, Pullman, Wash.
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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 and mi ≠ 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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 514 - 519
Copyright
Copyright © Canadian Mathematical Society 1967

References

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