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Found problems: 1

2019 Bundeswettbewerb Mathematik, 4
In the decimal expansion of $\sqrt{2}=1.4142\dots$, Isabelle finds a sequence of $k$ successive zeroes where $k$ is a positive integer. Show that the first zero of this sequence can occur no earlier than at the $k$-th position after the decimal point.
sqrt digit number theory digits sequences