Sums of Liouville type over primitive pairs and quadruples and some integer representations

Mohamed El Bachraoui

doi:10.1016/j.jnt.2012.06.009

Sums of Liouville type over primitive pairs and quadruples and some integer representations

Mohamed El Bachraoui

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

We prove identities of Liouville type on sums of even integer functions ranging over sets of relatively prime pairs and relatively prime quadruples. Among applications, we shall count the number of solutions of the Diophantine equations (a + c). x + (b + d). y = n and k(a + c). x + l(b + d). y = n in positive integers under certain relative primality conditions.

Original language	English
Pages (from-to)	226-241
Number of pages	16
Journal	Journal of Number Theory
Volume	133
Issue number	1
DOIs	https://doi.org/10.1016/j.jnt.2012.06.009
Publication status	Published - Jan 2013

Keywords

Arithmetic sums
Integer representations
Liouville's formulas

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jnt.2012.06.009

Cite this

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abstract = "We prove identities of Liouville type on sums of even integer functions ranging over sets of relatively prime pairs and relatively prime quadruples. Among applications, we shall count the number of solutions of the Diophantine equations (a + c). x + (b + d). y = n and k(a + c). x + l(b + d). y = n in positive integers under certain relative primality conditions.",

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AB - We prove identities of Liouville type on sums of even integer functions ranging over sets of relatively prime pairs and relatively prime quadruples. Among applications, we shall count the number of solutions of the Diophantine equations (a + c). x + (b + d). y = n and k(a + c). x + l(b + d). y = n in positive integers under certain relative primality conditions.

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KW - Liouville's formulas

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Sums of Liouville type over primitive pairs and quadruples and some integer representations

Abstract

Keywords

ASJC Scopus subject areas

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