An arithmetic term for the factorial function

Mihai Prunescu; Lorenzo Sauras-Altuzarra

doi:10.1016/j.exco.2024.100136

An arithmetic term for the factorial function

Mihai Prunescu
, Lorenzo Sauras-Altuzarra^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

As proved by Marchenkov and Mazzanti, every Kalmar function can be represented by arithmetic terms. We display one of such terms to represent the factorial function, and as a consequence, we get an example of an arithmetic term which represents a function whose image is the set of primes.

Original language	English
Article number	100136
Journal	Examples and Counterexamples
Volume	5
DOIs	https://doi.org/10.1016/j.exco.2024.100136
State	Published - Jun 2024
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2024 The Author(s)

Keywords

Elementary function
Fermat number
Kalmar function
Prime-generating function
Wilson's theorem

ASJC Scopus subject areas

Applied Mathematics
Mathematics (miscellaneous)
Computational Mathematics

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title = "An arithmetic term for the factorial function",

abstract = "As proved by Marchenkov and Mazzanti, every Kalmar function can be represented by arithmetic terms. We display one of such terms to represent the factorial function, and as a consequence, we get an example of an arithmetic term which represents a function whose image is the set of primes.",

keywords = "Elementary function, Fermat number, Kalmar function, Prime-generating function, Wilson's theorem",

author = "Mihai Prunescu and Lorenzo Sauras-Altuzarra",

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year = "2024",

month = jun,

doi = "10.1016/j.exco.2024.100136",

language = "English",

volume = "5",

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T1 - An arithmetic term for the factorial function

AU - Prunescu, Mihai

AU - Sauras-Altuzarra, Lorenzo

PY - 2024/6

Y1 - 2024/6

N2 - As proved by Marchenkov and Mazzanti, every Kalmar function can be represented by arithmetic terms. We display one of such terms to represent the factorial function, and as a consequence, we get an example of an arithmetic term which represents a function whose image is the set of primes.

AB - As proved by Marchenkov and Mazzanti, every Kalmar function can be represented by arithmetic terms. We display one of such terms to represent the factorial function, and as a consequence, we get an example of an arithmetic term which represents a function whose image is the set of primes.

KW - Elementary function

KW - Fermat number

KW - Kalmar function

KW - Prime-generating function

KW - Wilson's theorem

UR - https://www.scopus.com/pages/publications/85184013580

U2 - 10.1016/j.exco.2024.100136

DO - 10.1016/j.exco.2024.100136

M3 - Article

AN - SCOPUS:85184013580

SN - 2666-657X

VL - 5

JO - Examples and Counterexamples

JF - Examples and Counterexamples

M1 - 100136

ER -

An arithmetic term for the factorial function

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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