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Covering systems of congruences, a negative result
Published online by Cambridge University Press: 26 February 2010
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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 ≤ i ≤ k, we say that m is a covering number. We shall use the symbol ℕ to denote the natural numbers together with zero, then m is a covering number if, for each q there is an aq such that
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