Consecutive square-free numbers and square-free primitive roots

DOI10.1142/S1793042122500154zbMath1489.11005OpenAlexW3180045048WikidataQ114071927 ScholiaQ114071927MaRDI QIDQ5025448

Huaning Liu, Mengyao Jing

Publication date: 2 February 2022

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s1793042122500154

zbMATH Keywords

square-freecharacter sumKloosterman sumprimitive root

Mathematics Subject Classification ID

Congruences; primitive roots; residue systems (11A07) Estimates on character sums (11L40) Distribution of integers with specified multiplicative constraints (11N25)

Related Items (2)

Counting square-free integers represented by binary quadratic forms of a fixed discriminant ⋮ Square-free numbers of the form \(x^2+y^2+z^2+z+1\) and \(x^2+y^2+z+1\)

Cites Work

• On the number of pairs of positive integers \(x,y \leq H\) such that \(x^2+y^2+1\) is squarefree
• The square sieve and consecutive square-free numbers
• On the distribution of consecutive square-free primitive roots modulo p
• On the number of pairs of positive integers $x, y \leq H$ such that $x^2+y^2+1$, $x^2+y^2+2$ are square-free
• ON THE EXPONENTIAL SUM WITH SQUARE-FREE NUMBERS
• On finite pseudorandom binary sequences I: Measure of pseudorandomness, the Legendre symbol
• On the distribution of consecutive square-free numbers of the form $\mathbf{[\alpha n, [\alpha n]+1}$]
• CONSECUTIVE SQUARE-FREE NUMBERS OF THE FORM [nc, [nc] + 1]
• THE MEAN-VALUES OF ARITHMETICAL FUNCTIONS

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