Vol. 249, No. 2, 2011

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On the number of pairs of positive integers x1,x2 H such that x1x2 is a k-th power

Doychin I. Tolev

Vol. 249 (2011), No. 2, 495–507
Abstract

We find an asymptotic formula for the number of pairs of positive integers x1,x2 H such that the product x1x2 is a k-th power.

Keywords
counting solutions of Diophantine equations
Mathematical Subject Classification 2000
Primary: 11D45
Milestones
Received: 17 September 2009
Accepted: 4 January 2010
Published: 1 February 2011
Authors
Doychin I. Tolev
Faculty of Mathematics and Informatics
Sofia University “St. Kl. Ohridsky”
5 J.Bourchier
1164 Sofia
Bulgaria
http://www.tolev.org/