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Partitions with Restricted Summands or “the Money Changing Problem” Read chapter Read first chapter

2014 | OriginalPaper | Chapter

2. The Asymptotic Density of Relatively Prime Pairs and of Square-Free Numbers

Author : Ross G. Pinsky

Published in: Problems from the Discrete to the Continuous

Publisher: Springer International Publishing

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Abstract

Pick a positive integer at random. What is the probability of it being even? As stated, this question is not well posed, because there is no uniform probability measure on the set \(\mathbb{N}\) of positive integers. However, what one can do is fix a positive integer n, and choose a number uniformly at random from the finite set [n] = { 1, …, n}. Letting

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previous chapter Partitions with Restricted Summands or “the Money Changing Problem”
next chapter A One-Dimensional Probabilistic Packing Problem
Literature
27.
Nathanson, M.: Elementary Methods in Number Theory. Graduate Texts in Mathematics, vol. 195. Springer, New York (2000)
33.
Tenenbaum, G.: Introduction to Analytic and Probabilistic Number Theory. Cambridge Studies in Advanced Mathematics, vol. 46. Cambridge University Press, Cambridge (1995)
Metadata
Title
The Asymptotic Density of Relatively Prime Pairs and of Square-Free Numbers
Author
Ross G. Pinsky
Copyright Year
2014
Book
Problems from the Discrete to the Continuous

Print ISBN: 978-3-319-07964-6

Electronic ISBN: 978-3-319-07965-3

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-319-07965-3_2