Theorems · Theorem · number theory
jacobiSym.eq_neg_one_at_prime_divisor_of_eq_neg_one
∀ {a : ℤ} {n : ℕ}, jacobiSym a n = -1 → ∃ p, Nat.Prime p ∧ p ∣ n ∧ jacobiSym a p = -1If J(a | n) = -1, then n has a prime divisor p such that J(a | p) = -1.
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- Foundations
- Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
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- jacobiSym.zero_rightproof · cited by 4
- Nat.pos_of_mem_primeFactorsListproof · cited by 3
- jacobiSym.list_prod_rightproof · cited by 1
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