Rational points in Cantor sets (Q2735220)
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scientific article; zbMATH DE number 1640212
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Rational points in Cantor sets |
scientific article; zbMATH DE number 1640212 |
Statements
10 July 2002
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dyadic rationals
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triadic Cantor set
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Euler function
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0.90332884
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0.90002805
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Rational points in Cantor sets (English)
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This short note proves that for a given prime integer \(p> 3\) there are only finitely many fractions the denominator of which is a power of \(p\), which are contained in the classical triadic Cantor set. Furthermore, if 3 is a primitive root modulo \(p^2\), then no such fraction lies in the Cantor set. The proof is based on basic arithmetic results on the Euler function.
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