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# Group of integers

DOI link for Group of integers

Group of integers book

# Group of integers

DOI link for Group of integers

Group of integers book

BySandor Szabo, Arthur D. Sands

Edition 1st Edition

First Published 2009

Imprint Chapman and Hall/CRC

Pages 20

eBook ISBN 9780429143458

## ABSTRACT

A cyclic group of order n may be realized as the additive group Z/nZ, that is, as the integers modulo n. When we interpret Theorem 3.19 (on page 59) in this way we obtain the following result.

THEOREM 7.1

Let m and n be relatively prime positive integers. If A = {a1, . . . , am} and B = {b1, . . . , bn} are sets of integers such that their sum set

A+B = {ai + bj : 1 ≤ i ≤ m, 1 ≤ j ≤ n} is a complete set of representatives modulo mn, then A is a complete set of residues modulo m and B is a complete set of residues modulo n.