On rational approximations to Euler's constant  and to .

Elsner, Carsten

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For a positive integer $n$ we write $φ (n)$ for the Euler function of $n$ . In this note, we show that if $b > 1$ is a fixed positive integer, then the equation $φ (x \frac{b^{n} - 1}{b - 1}) = y \frac{b^{m} - 1}{b - 1}, where x, y \in {1, ..., b - 1},$ has only finitely many positive integer solutions $(x, y, m, n)$ .

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Displaying similar documents to “On rational approximations to Euler's constant γ and to γ + log ( a / b ) .”

Displaying similar documents to “On rational approximations to Euler's constant $γ$ and to $γ + log (a / b)$ .”