Squarefree smooth numbers and Euclidean prime generators

Andrew R. Booker; Carl Pomerance

doi:10.1090/proc/13576

Squarefree smooth numbers and Euclidean prime generators

Andrew R. Booker, Carl Pomerance

Research output: Contribution to journal › Article (Academic Journal) › peer-review

3 Citations (Scopus)

423 Downloads (Pure)

Abstract

We show that for each prime p > 7, every residue mod p can be represented by a squarefree number with largest prime factor at most p. We give two applications to recursive prime generators akin to the one Euclid used to prove the infinitude of primes.

Original language	English
Pages (from-to)	5035-5042
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	145
Issue number	12
Early online date	31 Aug 2017
DOIs	https://doi.org/10.1090/proc/13576
Publication status	Published - 1 Dec 2017

Access to Document

10.1090/proc/13576

Full-text PDF (accepted author manuscript)
This is the author accepted manuscript (AAM). The final published version (version of record) is available online via AMS at http://www.ams.org/journals/proc/0000-000-00/S0002-9939-2017-13576-X/home.html. Please refer to any applicable terms of use of the publisher.
Accepted author manuscript, 173 KB

Handle.net

Persistent link

Cite this

@article{566c03d9af1346d6a482fa38b4c01d06,

title = "Squarefree smooth numbers and Euclidean prime generators",

abstract = "We show that for each prime p > 7, every residue mod p can be represented by a squarefree number with largest prime factor at most p. We give two applications to recursive prime generators akin to the one Euclid used to prove the infinitude of primes.",

author = "Booker, \{Andrew R.\} and Carl Pomerance",

year = "2017",

month = dec,

day = "1",

doi = "10.1090/proc/13576",

language = "English",

volume = "145",

pages = "5035--5042",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "12",

}

TY - JOUR

T1 - Squarefree smooth numbers and Euclidean prime generators

AU - Booker, Andrew R.

AU - Pomerance, Carl

PY - 2017/12/1

Y1 - 2017/12/1

N2 - We show that for each prime p > 7, every residue mod p can be represented by a squarefree number with largest prime factor at most p. We give two applications to recursive prime generators akin to the one Euclid used to prove the infinitude of primes.

AB - We show that for each prime p > 7, every residue mod p can be represented by a squarefree number with largest prime factor at most p. We give two applications to recursive prime generators akin to the one Euclid used to prove the infinitude of primes.

UR - https://www.scopus.com/pages/publications/85032946108

U2 - 10.1090/proc/13576

DO - 10.1090/proc/13576

M3 - Article (Academic Journal)

AN - SCOPUS:85032946108

SN - 0002-9939

VL - 145

SP - 5035

EP - 5042

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 12

ER -

Squarefree smooth numbers and Euclidean prime generators

Abstract

Access to Document

Handle.net

Other files and links

Fingerprint

Cite this