On sums and products of residues modulo p
A. Sárközy (2005)
Acta Arithmetica
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A. Sárközy (2005)
Acta Arithmetica
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Mariusz Skałba (2003)
Colloquium Mathematicae
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The product of consecutive integers cannot be a power (after Erdős and Selfridge), but products of disjoint blocks of consecutive integers can be powers. Even if the blocks have a fixed length l ≥ 4 there are many solutions. We give the bound for the smallest solution and an estimate for the number of solutions below x.
Alfred Moessner, George Xeroudakes (1954)
Publications de l'Institut Mathématique
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R. B. Sher (1975)
Colloquium Mathematicae
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Akira Takaku (1987)
Colloquium Mathematicae
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Vsevolod F. Lev (2008)
Acta Arithmetica
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Sakmar, I.A. (2003)
APPS. Applied Sciences
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A. Wojciechowska (1969)
Colloquium Mathematicae
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Zhefeng Xu, Wenpeng Zhang (2008)
Acta Arithmetica
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Koichi Kawada, Trevor D. Wooley (2002)
Acta Arithmetica
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Victor J. W. Guo, Frédéric Jouhet, Jiang Zeng (2007)
Acta Arithmetica
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Henri Virtanen (2002)
Acta Arithmetica
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Zhi-Wei Sun (2001)
Acta Arithmetica
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William Ellison (2013)
Acta Arithmetica
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If K is a field, denote by P(K,k) the a ∈ K which are sums of kth powers of elements of K, by P⁺(K,k) the set of a ∈ K which are sums of kth powers of totally positive elements of K. We give some simple conditions for which there exist integers w(K,k) and g(K,k) such that: a ∈ P(K,k) implies that a is the sum of at most w(K,k) kth powers; a ∈ P⁺(K,k) implies that a is the sum of at most g(K,k) totally positive kth powers. We apply the results to characterise functions that are sums of...
R. B. Sher (1979)
Colloquium Mathematicae
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Li Xiaoxue, Hu Jiayuan (2017)
Open Mathematics
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The main purpose of this paper is using the analytic method and the properties of the classical Gauss sums to study the computational problem of one kind fourth hybrid power mean of the quartic Gauss sums and Kloosterman sums, and give an exact computational formula for it.
Huaning Liu, Wenpeng Zhang (2007)
Acta Arithmetica
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