Hi Alexander,

Theorem ~ lgsquadlem2 seems to be similar to Gauss' Lemma. Wikipedia
also mentions it
<https://en.wikipedia.org/wiki/Proofs_of_quadratic_reciprocity#Eisenstein's_proof>
in its entry on Eisenstein proof of the quadratic reciprocity: /This
result is very similar to Gauss's lemma, and can be proved in a similar
fashion./

After a bit more consideration though, it does not seem to me that it is
easy to derive Gauss' lemma from it. This would leave you with proving
Gauss' lemma.

Or, if you don't mind cooperation, you could call for someone in the
community to prove Gauss' lemma while you continue on Fermat numbers.

BR,
_
Thierry

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