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On Gaps Between Squarefree Numbers II

โœ Scribed by Filaseta, M.; Trifonov, O.


Book ID
120094821
Publisher
Oxford University Press
Year
1992
Tongue
English
Weight
145 KB
Volume
s2-45
Category
Article
ISSN
0024-6107

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On Gaps Between k-Free Numbers
โœ O. Trifonov ๐Ÿ“‚ Article ๐Ÿ“… 1995 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 337 KB

An elementary proof is given that for \(k \geqslant 3\) there exists a constant \(c=c(k)\) such that for \(x\) sufficiently large (depending on \(k\) ), the interval \(\left(x, x+c x^{1,12 k+1} \log x\right.\) ] contains a \(k\)-free number. This result improves on a previous result of M. Filaseta (