Is there a non-square positive integer $n$, that $\sqrt{n}$ has only even digits in its decimal representation ?
2026-04-01 12:46:12.1775047572
Square root of an integer has only even digits
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No such $n$ is known.
If one were found, it would be the biggest shock in Mathematics since, well, maybe since ever; certainly, since Godel's incompleteness results.
No proof is known that such an $n$ does not exist.