Then he remembered the commenter’s name: mod7_legendre . Adrien-Marie Legendre. Number theorist. Best known for… the Legendre symbol. And the law of quadratic reciprocity. Fermat’s little theorem. But 1682? Fermat died in 1665.

He read until dawn. Through the Euclidean algorithm ("like peeling an onion"). Through the linear Diophantine equation (ax + by = c). When the sun hit the barred window, he was on Chapter 5: Fermat’s Little Theorem. The proof felt like a door swinging open.

The password was samuel_1682 .

At 7 AM, he walked upstairs to his dorm room. His roommate, Derek, was still asleep. Leo booted up Gauss, opened a LaTeX editor, and started writing his own proof. Not for the exam—for himself. Professor Varner handed back the midterms on Thursday. Leo’s grade: 94. But that wasn’t the good part. At the bottom of the last page, Varner had written in red pen:

He closed his eyes. 1682. What happened in 1682? He pulled out his phone, shaky connection, Wikipedia: 1682 – Gottfried Leibniz publishes the first paper on calculus. Not relevant. Then: 1682 – Fermat’s son, Samuel, publishes a new edition of his father’s work, including the famous margin note about the Last Theorem.