Problem 3 of Dubickas (2006): Is $\sqrt{3} \in \mathcal{Z}$?

Answers Problem 3 and generalizes it: the classification $\sqrt{m} \in \mathcal{S} \iff m = 2$ covers every square root, and a further theorem replaces parity by divisibility by any $p \ge 2$. Note the scope of the machine-checking, which is narrower than the paper: the author states that the case $m = 3$ is what is verified in Lean, and the repository flags the thickness computation of section 4.1 and all of section 8 as not formalized.

Answers Problem 3 and generalizes it: the classification $\sqrt{m} \in \mathcal{S} \iff m = 2$ covers every square root, and a further theorem replaces parity by divisibility by any $p \ge 2$. Note the scope of the machine-checking, which is narrower than the paper: the author states that the case $m = 3$ is what is verified in Lean, and the repository flags the thickness computation of section 4.1 and all of section 8 as not formalized.