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- W2000351815 abstract "This paper contains an elementary derivation of formulas for multiplicative functions of<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$m$><mml:mi>m</mml:mi></mml:math>which exactly yield the following numbers: the number of distinct arithmetic progressions of<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$w$><mml:mi>w</mml:mi></mml:math>reduced residues modulo<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$m$><mml:mi>m</mml:mi></mml:math>; the number of the same with first term<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$n$><mml:mi>n</mml:mi></mml:math>; the number of the same with mean<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$n><mml:mi>n</mml:mi></mml:math>; the number of the same with common difference<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$n$><mml:mi>n</mml:mi></mml:math>. With<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$m$><mml:mi>m</mml:mi></mml:math>and odd<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$w$><mml:mi>w</mml:mi></mml:math>fixed, the values of the first two of the last three functions are fixed and equal for all<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$n$><mml:mi>n</mml:mi></mml:math>relatively prime to<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$m$><mml:mi>m</mml:mi></mml:math>; other similar relations exist among these three functions." @default.
- W2000351815 created "2016-06-24" @default.
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- W2000351815 date "2001-01-01" @default.
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- W2000351815 title "Arithmetic progressions that consist only of reduced residues" @default.
- W2000351815 cites W1967061303 @default.
- W2000351815 doi "https://doi.org/10.1155/s0161171201006123" @default.
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