On sums of three squares
Jan Wójcik (1971)
Colloquium Mathematicae
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Jan Wójcik (1971)
Colloquium Mathematicae
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James G. Huard, Kenneth S. Williams (2003)
Acta Arithmetica
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Roger Clement Crocker (2008)
Colloquium Mathematicae
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It can be shown that the positive integers representable as the sum of two squares and one power of k (k any fixed integer ≥ 2) have positive density, from which it follows that those integers representable as the sum of two squares and (at most) two powers of k also have positive density. The purpose of this paper is to show that there is an infinity of positive integers not representable as the sum of two squares and two (or fewer) powers of k, k again any fixed integer ≥ 2. ...
Zhi-Wei Sun (2007)
Acta Arithmetica
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Tsz Ho Chan (2006)
Acta Arithmetica
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Jagy, William C., Kaplansky, Irving (1995)
Experimental Mathematics
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Jörg Brüdern (2014)
Bulletin of the Polish Academy of Sciences. Mathematics
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Asymptotic formulae are provided for the number of representations of a natural number as the sum of four and of three squares that are pairwise coprime.
Hickerson, Dean, Kleber, Michael (1999)
Journal of Integer Sequences [electronic only]
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Heng Huat Chan, Shaun Cooper, Wen-Chin Liaw (2008)
Acta Arithmetica
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Andrew Bremner (2001)
Acta Arithmetica
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Jianya Liu, Tao Zhan (2001)
Acta Arithmetica
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Ikramov, Kh.D., Matin Far, M. (2004)
Zapiski Nauchnykh Seminarov POMI
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Paul Rowe (2005)
Acta Arithmetica
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John Pais, Richard Singer (2004)
Visual Mathematics
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Ratko Tošić (1980)
Publications de l'Institut Mathématique
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A. Schinzel (2013)
Bulletin of the Polish Academy of Sciences. Mathematics
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It is proved that all sufficiently large integers satisfying the necessary congruence conditions mod 24 are sums of four squares prime in pairs.
M. Kuczma (1969)
Annales Polonici Mathematici
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D.W. Lewis (1985)
Mathematische Zeitschrift
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