A Connection between Covers of Z and Unit Fractions
نویسندگان
چکیده
is usually called the covering function of A. Clearly wA(x) is periodic modulo the least common multiple NA of the moduli n1, . . . , nk. As in [S99] we call m(A) = minx∈Z wA(x) the covering multiplicity of A. Let m ∈ Z. If wA(x) > m for all x ∈ Z, then we call A an m-cover of Z. If A is an m-cover of Z but At = {as(ns)}s∈[1,k]\{t} is not (where [a, b] = {x ∈ Z : a 6 x 6 b} for a, b ∈ Z), then we say that A forms an m-cover of Z with at(nt) irredundant. If wA(x) = m for all x ∈ Z, then A is said to be an exact m-cover of Z.
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