Mathematika

Research Article

Covering systems of congruences, a negative result

J. A. Haighta1

a1 Department of Mathematics, University College, London.

Suppose that we have a system of congruences ai (mod ni) 1 < n1 < … < ni < … < nk such that every integer is congruent to at least one ai (mod ni), then we say that it is a covering system of congruences. If ni | m, 1 ≤ ik, we say that m is a covering number. We shall use the symbol to denote the natural numbers together with zero, then m is a covering number if, for each q there is an aq such that

S0025579300009608_eqnU1

(Received May 03 1978)

Key Words:

  • 10L99: NUMBER THEORY; Sequence of integers