On the radical of a perfect number.
Luca, Florian, Pomerance, Carl (2010)
The New York Journal of Mathematics [electronic only]
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Luca, Florian, Pomerance, Carl (2010)
The New York Journal of Mathematics [electronic only]
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Olaru, Elefterie, Mandrescu, Eugen, Ion, Cristian, Anastasoaei, Vasile (2005)
Acta Universitatis Apulensis. Mathematics - Informatics
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Evans, M.J., Humke, P.D. (2003)
Acta Mathematica Universitatis Comenianae. New Series
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Ireneusz Recław (1991)
Colloquium Mathematicae
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Arnold Miller, Strashimir Popvassilev (2000)
Fundamenta Mathematicae
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We give examples of a Vitali set and a Hamel basis which are Marczewski measurable and perfectly dense. The Vitali set example answers a question posed by Jack Brown. We also show there is a Marczewski null Hamel basis for the reals, although a Vitali set cannot be Marczewski null. The proof of the existence of a Marczewski null Hamel basis for the plane is easier than for the reals and we give it first. We show that there is no easy way to get a Marczewski null Hamel basis for the reals...
Dharmanand Baboolal (2011)
Czechoslovak Mathematical Journal
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Perfect compactifications of frames are introduced. It is shown that the Stone-Čech compactification is an example of such a compactification. We also introduce rim-compact frames and for such frames we define its Freudenthal compactification, another example of a perfect compactification. The remainder of a rim-compact frame in its Freudenthal compactification is shown to be zero-dimensional. It is shown that with the assumption of the Boolean Ultrafilter Theorem the Freudenthal compactification...
Tsereteli, I. (1994)
Georgian Mathematical Journal
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Bege, Antal, Fogarasi, Kinga (2009)
Acta Universitatis Sapientiae. Mathematica
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J. Brendle, P. Larson, S. Todorčević (2008)
Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques
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