Article ID Journal Published Year Pages File Type
4594895 Journal of Number Theory 2009 21 Pages PDF
Abstract

TextFinding a function which generates a sequence via iteration whose values at one or many points in its domain satisfy certain prescribed properties, i.e., finding a function such that the Picard orbit(s) of one or many points in its domain which possess some given properties, is an interesting problem. Given any positive integer n greater than one, we construct in this paper families of functions on the natural numbers such that the sequence of the iterations of each of these functions at any positive integer s contains infinitely many perfect n-powers. In terms of Picard sequences, this amounts to constructing a function whose Picard orbit at every point in its domain contains infinitely many perfect n-powers.VideoFor a video summary of this paper, please visit http://www.youtube.com/watch?v=wJqaXyB2pdo.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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