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The Quarterly Journal of Mathematics 2000 51(3):343-352; doi:10.1093/qjmath/51.3.343
© 2000 by Oxford University Press
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The least common multiple and lattice points on hyperbolas

Andrew Granville1,* and Jorge Jiménez-urroz2,§

1 Department of Mathematics, University of Georgia, Athens, 30602, Georgia, USA 2 Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049, Madrid, España

We bound, from below, the least common multiple of k integers from a short interval. This is used to bound the length of an arc {Gamma} of the hyperbola, xy = N, containing k integer lattice points.

Received 12 May, 1998. Revised 12 May, 1998.

* E-mail: hmsri@uvvm.uvic.ca

§ E-mail: vu@math-1.sci.kuniv.edu.kw


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