A generalization of the Chinese remainder theorem

B. Arazi

Vol. 70 (1977), No. 2, 289–296

DOI: 10.2140/pjm.1977.70.289

Abstract

Let X be a set of r nonnegative integers, and let B_i i = 1,2,3,⋯,t be the unordered sets of residues of the elements of X modulo m_i, where it is not known which element in X produces a given element in B_i.

For the case where r = 1, the Chinese Remainder Theorem introduces necessary and sufficient conditions on the values of m_i in order that X may have a unique solution mod ∏ _i=1^tm_i.

This paper introduces such conditions for the case where r ≧ 1.

Mathematical Subject Classification

Primary: 10A10, 10A10

Milestones

Received: 23 August 1976

Revised: 8 February 1977

Published: 1 June 1977