Multiplicative Structure of Values of the Euler Function

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Multiplicative Structure of Values of the Euler Function

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[-] show simple item record Banks, William David, 1964- Friedlander, J. B. (John B.) Pomerance, Carl Shparlinski, Igor E. 2011-05-05T17:29:19Z 2011-05-05T17:29:19Z 2004
dc.description This is a preprint of a book chapter published in High Primes and Misdemeanours: Lectures in Honour of the 60th Birthday of Hugh Cowie Williams, Fields Institute Communications, AMS (2004). © American Mathematical Society. en_US
dc.description.abstract We establish upper bounds for the number of smooth values of the Euler function. In particular, although the Euler function has a certain “smoothing” effect on its integer arguments, our results show that, in fact, most values produced by the Euler function are not smooth. We apply our results to study the distribution of “strong primes”, which are commonly encountered in cryptography. We also consider the problem of obtaining upper and lower bounds for the number of positive integers n ≤ x for which the value of the Euler function φ (n) is a perfect square and also for the number of n ≤ x such that φ (n) is squarefull. We give similar bounds for the Carmichael function λ (n). en_US
dc.language.iso en_US en_US
dc.relation.ispartof Mathematics publications (MU) en
dc.source.uri en_US
dc.subject.lcsh Cryptography en_US
dc.subject.lcsh Number theory en_US
dc.title Multiplicative Structure of Values of the Euler Function en_US
dc.type Preprint en_US
dc.relation.ispartofcommunity University of Missouri-Columbia. College of Arts and Sciences. Department of Mathematics

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