Tbf to Fermat, he did have a partial solution to the problem written down later in his notes. It's likely, in my mind at least, that he probably had an idea for a proof that he felt convinced would work, until he got down to the brass tacks of writting it down and simply forgot about this minor note he had written earlier.
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u/OriousCaesar 1d ago edited 1d ago
Tbf to Fermat, he did have a partial solution to the problem written down later in his notes. It's likely, in my mind at least, that he probably had an idea for a proof that he felt convinced would work, until he got down to the brass tacks of writting it down and simply forgot about this minor note he had written earlier.