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Omni-MATH / Find digits x,y,z such that the equality

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Find digits x,y,zx, y, z such that the equality \[\sqrt{\underbrace{\overline{xx\cdots x}}_{2n \text{ times}}-\underbrace{\overline{yy\cdots y}}_{n \text{ times}}}=\underbrace{\overline{zz\cdots z}}_{n \text{ times}}\] holds for at least two values of $n \in \mathbb N$, and in that case find all nn for which this equality is true.
Plain-text mathematical notation (without MathML)
Find digits x,y,z such that the equality
\[\sqrt{\underbrace{\overline{xx\cdots x}}_{2n \text{ times}}-\underbrace{\overline{yy\cdots y}}_{n \text{ times}}}=\underbrace{\overline{zz\cdots z}}_{n \text{ times}}\]
holds for at least two values of $n \in \mathbb N$, and in that case find all n for which this equality is true.
Original LaTeX notation
Find digits $x, y, z$ such that the equality
\[\sqrt{\underbrace{\overline{xx\cdots x}}_{2n \text{ times}}-\underbrace{\overline{yy\cdots y}}_{n \text{ times}}}=\underbrace{\overline{zz\cdots z}}_{n \text{ times}}\]
holds for at least two values of $n \in \mathbb N$, and in that case find all $n$ for which this equality is true.

Discussion

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Source and history

task_id
cf512fab-2680-5ba5-af63-6757adb7180e
task_key
test--cf512fab-2680-5ba5-af63-6757adb7180e
task_revision_id
1
config / split
/ test

Official source

initial import