On the density of odd integers of the form \((p-1)2^{-n}\) and related questions (Q1257043)
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scientific article; zbMATH DE number 3629060
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the density of odd integers of the form \((p-1)2^{-n}\) and related questions |
scientific article; zbMATH DE number 3629060 |
Statements
On the density of odd integers of the form \((p-1)2^{-n}\) and related questions (English)
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1979
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Given \(k\) primes \(p_1,\dots,p_k\), write \(p-1=p_1^{a_1}\dots p_k^{a_k}s_p\), where \(s_p\) is coprime to \(P=p_1p_2\dots p_k\). It is proved that the sequence of numbers occurring as \(s_p\) for some prime \(p\) has positive lower density. The most interesting unsolved problem is whether this sequence (\(s_p\)) can contain all numbers, coprime to \(P\); concerning this question some numerical data are given.
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primes of special form
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divisors
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sieve methods
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density
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0.9318433
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0.92164433
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0.9107489
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