, Volume 67, Issue 1, pp 187-195

Sur le developpement de \(\sqrt m\) en fraction continue p-adiqueen fraction continue p-adique

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Abstract

This note deals with the Mahler-Browkin p-adic continued fractions. The principal result is the following:

For any prime p>2 and for any d ∈ ℕ, d odd, there are only finitely many m ∈ ℤ such that the p-adic continued fraction expansion of \(\sqrt m\) ∈ ℚp is periodic with period of length d.