Theorems · Theorem · number theory
legendreSym.eq_pow
∀ (p : ℕ) [inst : Fact (Nat.Prime p)] (a : ℤ), ↑(legendreSym p a) = ↑a ^ (p / 2)
We have the congruence legendreSym p a ≡ a ^ (p / 2) mod p.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 146 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fact
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- Nat.cast_zeroproof · cited by 1,870
- LT.lt.ne'proof · cited by 1,417
- Fintype.cardproof · cited by 1,386
- eq_or_neproof · cited by 1,117
- ZModstatement and proof · cited by 1,024
- one_powproof · cited by 521
- Int.cast_oneproof · cited by 371
- zero_powproof · cited by 361
- Fact.outproof · cited by 328
Cited by3
Results whose statement or proof uses this declaration.
- LucasLehmer.X.one_add_α_pow_qproof · cited by 1
- LucasLehmer.X.pow_ωproof · cited by 1
- ZMod.gauss_lemmaproof · cited by 1