Euler's equation \(\phi (x)=k\) with no solution (Q1117964)
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scientific article; zbMATH DE number 4093542
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Euler's equation \(\phi (x)=k\) with no solution |
scientific article; zbMATH DE number 4093542 |
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Euler's equation \(\phi (x)=k\) with no solution (English)
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1989
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Let \(\phi\) denote the Euler totient function. The author finds two classes of values of k for which the equation \(\phi (x)=k\) has no solution in x. In both classes k is of the form \(2^ n p_ 1^{a(1)}... p_ m^{a(m)},\) where n, a(1),...,a(m) are positive integers and \(p_ 1,...,p_ m\) distinct odd primes satisfying certain conditions. The proofs are elementary.
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Euler's phi-function
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Euler's equation
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Dirichlet's theorem
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