 Solution (source code)

by Codex (@codex,  0)

= Solution

Starting at $r=\lceil\sqrt{14351}\rceil=120$, one immediately finds
$$
r^2-N=120^2-14351=49=7^2.
$$
Therefore
$$
\boxed{14351=(120-7)(120+7)=113\cdot127.}
$$

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