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Products of three pairwise coprime integers in short intervals

Part of: Multiplicative number theory

Published online by Cambridge University Press:  01 April 2012

Asim Islam
Asim Islam*
Affiliation:
Department of Mathematics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, United Kingdom (email: [email protected])

Abstract

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The existence of products of three pairwise coprime integers is investigated in short intervals of the form . A general theorem is proved which shows that such integer products exist provided there is a bound on the product of any two of them. A particular case of relevance to elliptic curve cryptography, where all three integers are of order , is presented as a corollary to this result.

MSC classification

Secondary: 11N25: Distribution of integers with specified multiplicative constraints
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 15 , May 2012 , pp. 59 - 70
Copyright
Copyright © London Mathematical Society 2012

References

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