Generalized Schatunowsky theorem in a weak arithmetic

Fuente: arXiv
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Main Authors: King, Hala, Pambuccian, Victor
Format: Preprint
Published: 2025
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author King, Hala
Pambuccian, Victor
author_facet King, Hala
Pambuccian, Victor
contents Schatunowsky's 1893 theorem, that 30 is the largest number all of whose totatives are primes, has been recently generalized by Kaneko and Nakai. In its generalized form, it states the finiteness of the set of all positive numbers $n$, which, for a fixed prime $p$, have the property that all of $n$'s totatives that are not divisible by any prime less than or equal to $p$ are prime numbers. It is this generalized form that we show holds in a weak arithmetic
format Preprint
id arxiv_https___arxiv_org_abs_2506_08256
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Generalized Schatunowsky theorem in a weak arithmetic
King, Hala
Pambuccian, Victor
Logic
03B30 03C62 03H15 11A41
Schatunowsky's 1893 theorem, that 30 is the largest number all of whose totatives are primes, has been recently generalized by Kaneko and Nakai. In its generalized form, it states the finiteness of the set of all positive numbers $n$, which, for a fixed prime $p$, have the property that all of $n$'s totatives that are not divisible by any prime less than or equal to $p$ are prime numbers. It is this generalized form that we show holds in a weak arithmetic
title Generalized Schatunowsky theorem in a weak arithmetic
topic Logic
03B30 03C62 03H15 11A41
url https://arxiv.org/abs/2506.08256