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• W1970594294 abstract "An infinite sequence <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=a 1 greater-than a 2 greater-than midline-horizontal-ellipsis> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>a</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>></mml:mo> <mml:msub> <mml:mi>a</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>></mml:mo> <mml:mo>⋯<!-- ⋯ --></mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>a_1>a_2>dotsb</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=d> <mml:semantics> <mml:mi>d</mml:mi> <mml:annotation encoding=application/x-tex>d</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-<italic>complete</italic> if every sufficiently large integer is the sum of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=a Subscript i> <mml:semantics> <mml:msub> <mml:mi>a</mml:mi> <mml:mi>i</mml:mi> </mml:msub> <mml:annotation encoding=application/x-tex>a_i</mml:annotation> </mml:semantics> </mml:math> </inline-formula> such that no one divides the other. We investigate <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=d> <mml:semantics> <mml:mi>d</mml:mi> <mml:annotation encoding=application/x-tex>d</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-completeness of sets of the form <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-brace p Superscript alpha Baseline q Superscript beta Baseline right-brace> <mml:semantics> <mml:mrow> <mml:mo fence=false stretchy=false>{</mml:mo> <mml:msup> <mml:mi>p</mml:mi> <mml:mi>α<!-- α --></mml:mi> </mml:msup> <mml:msup> <mml:mi>q</mml:mi> <mml:mi>β<!-- β --></mml:mi> </mml:msup> <mml:mo fence=false stretchy=false>}</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>{p^alpha q^beta }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-brace p Superscript alpha Baseline q Superscript beta Baseline r Superscript gamma Baseline right-brace> <mml:semantics> <mml:mrow> <mml:mo fence=false stretchy=false>{</mml:mo> <mml:msup> <mml:mi>p</mml:mi> <mml:mi>α<!-- α --></mml:mi> </mml:msup> <mml:msup> <mml:mi>q</mml:mi> <mml:mi>β<!-- β --></mml:mi> </mml:msup> <mml:msup> <mml:mi>r</mml:mi> <mml:mi>γ<!-- γ --></mml:mi> </mml:msup> <mml:mo fence=false stretchy=false>}</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>{p^alpha q^beta r^gamma }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=alpha comma beta comma gamma> <mml:semantics> <mml:mrow> <mml:mi>α<!-- α --></mml:mi> <mml:mo>,</mml:mo> <mml:mi>β<!-- β --></mml:mi> <mml:mo>,</mml:mo> <mml:mi>γ<!-- γ --></mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>alpha ,beta ,gamma</mml:annotation> </mml:semantics> </mml:math> </inline-formula> nonnegative." @default.
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• W1970594294 date "1996-01-01" @default.
• W1970594294 modified "2023-10-17" @default.
• W1970594294 title "𝑑-complete sequences of integers" @default.
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• W1970594294 doi "https://doi.org/10.1090/s0025-5718-96-00707-7" @default.
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