# Arithmetic progressions, prime numbers, and squarefree integers

Stuart Clary; Jacek Fabrykowski

Czechoslovak Mathematical Journal (2004)

- Volume: 54, Issue: 4, page 915-927
- ISSN: 0011-4642

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topClary, Stuart, and Fabrykowski, Jacek. "Arithmetic progressions, prime numbers, and squarefree integers." Czechoslovak Mathematical Journal 54.4 (2004): 915-927. <http://eudml.org/doc/30910>.

@article{Clary2004,

abstract = {In this paper we establish the distribution of prime numbers in a given arithmetic progression $p \equiv l \hspace\{4.44443pt\}(mod \; k)$ for which $ap + b$ is squarefree.},

author = {Clary, Stuart, Fabrykowski, Jacek},

journal = {Czechoslovak Mathematical Journal},

keywords = {primes in arithmetic progressions; squarefree integers; Artin’s constant; primes in arithmetic progressions; squarefree integers; Artin's constant},

language = {eng},

number = {4},

pages = {915-927},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Arithmetic progressions, prime numbers, and squarefree integers},

url = {http://eudml.org/doc/30910},

volume = {54},

year = {2004},

}

TY - JOUR

AU - Clary, Stuart

AU - Fabrykowski, Jacek

TI - Arithmetic progressions, prime numbers, and squarefree integers

JO - Czechoslovak Mathematical Journal

PY - 2004

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 54

IS - 4

SP - 915

EP - 927

AB - In this paper we establish the distribution of prime numbers in a given arithmetic progression $p \equiv l \hspace{4.44443pt}(mod \; k)$ for which $ap + b$ is squarefree.

LA - eng

KW - primes in arithmetic progressions; squarefree integers; Artin’s constant; primes in arithmetic progressions; squarefree integers; Artin's constant

UR - http://eudml.org/doc/30910

ER -

## References

top- Introduction to Analytic Number Theory, Springer-Verlag, 1976. (1976) MR0434929
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- Concrete Mathematics: A Foundation for Computer Science, Addison-Wesley, second edition, 1994. (1994) MR1397498
- An Introduction to the Theory of Numbers, Oxford at the Clarendon Press, fourth edition, 1960. (1960)
- Handbuch der Lehre von der Verteilung der Primzahlen, Chelsea, New York, second edition, 1974. (1974)
- Private communication to Jacek Fabrykowski, 1989. (1989)
- 10.2307/2305811, Amer. Math. Monthly 56 (1949), 17–19. (1949) Zbl0033.16203MR0028335DOI10.2307/2305811
- Über die kleinste quadratfrei Zahl einer arithmetischen Reihe, Monatsh. Math. 3 (1958), 173–176. (1958) MR0092806
- Evaluation of Artin’s constant and the twin-prime constant, Math. Comp. 15 (1961), 396–398. (1961) MR0124305

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