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dc.contributor.authorBanks, William David, 1964-
dc.contributor.authorFriedlander, J. B. (John B.)
dc.contributor.authorPomerance, Carl
dc.contributor.authorShparlinski, Igor E.
dc.descriptionThis 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.abstractWe 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.relation.ispartofMathematics publications (MU)en
dc.relation.ispartofcommunityUniversity of Missouri-Columbia. College of Arts and Sciences. Department of Mathematics
dc.subject.lcshNumber theoryen_US
dc.titleMultiplicative Structure of Values of the Euler Functionen_US

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