A mechanical proof of Quadratic Reciprocity
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We describe the use of the Boyer-Moore theorem prover in mechanically generating a proof of the Law of Quadratic Reciprocity: for distinct odd primes p and q, the congruences x2≡q (mod p) and x2≡p (mod q) are either both solvable or both unsolvable, unless p≡q≡3 (mod 4). The proof is a formalization of an argument due to Eisenstein, based on a lemma of Gauss. The input to the theorem prover consists of nine function definitions, thirty conjectures, and various hints for proving them. The proofs are derived from a library of lemmas that includes Fermat's Theorem and the Gauss Lemma.
Key wordsAutomatic theorem proving Boyer-Moore prover number theory quadratic reciprocity
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