Sur le développement de \(\sqrt{m}\) en fraction continue p-adique. (On the expansion of \(\sqrt{m}\) in a p-adic continued fraction) (Q809140)

The Mahler-Browkin p-adic continued fraction admits partial quotients \(a/p^ b\) with \(a\in {\mathbb{Z}}\) and \(-p^{b+1}/2<a\leq p^{b+1}/2\). The author demonstrates that there are only finitely many \(m\in {\mathbb{Z}}\) so that the p-adic continued fraction expansion of \(\sqrt{m}\in {\mathbb{Q}}_ p\) is periodic with period of odd given length.