کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4594895 1335787 2009 21 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Picard sequences with every orbit containing infinitely many perfect n-powers
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Picard sequences with every orbit containing infinitely many perfect n-powers
چکیده انگلیسی

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 129, Issue 2, February 2009, Pages 381–401
نویسندگان
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