A special prime divisor of the sequence: \(ah+b,a(h+1)+b,\dots , a(h+k-1)+b\) (Q1187069)
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scientific article; zbMATH DE number 38593
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A special prime divisor of the sequence: \(ah+b,a(h+1)+b,\dots , a(h+k-1)+b\) |
scientific article; zbMATH DE number 38593 |
Statements
A special prime divisor of the sequence: \(ah+b,a(h+1)+b,\dots , a(h+k-1)+b\) (English)
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28 June 1992
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The following generalization of the well known theorem by Sylvester and Schur is proved: Let \(a\) and \(b\) be two relatively prime positive integers. Then for \(h>k\) and sufficiently large \(k\), at least one of the integers \(ah+b\), \(a(h+1)+b,\ldots,a(h+k-1)+b\) is divisible by a prime \(p\) such that \(p>ak+b\).
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divisors of consecutive integers
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prime number theorem
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Sylvester-Schur- theorem
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0.8221138715744019
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0.7659782767295837
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0.7659782767295837
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