Theorems · Theorem · number theory
Choose.eq_pow_multiplicity_of_choose_modEq_zero
∀ {n p : ℕ} [Fact (Nat.Prime p)],
0 < n → (∀ i ∈ Finset.Icc 1 (n - 1), ↑(n.choose i) ≡ 0 [ZMOD ↑p]) → n = p ^ multiplicity p nFor primes p and positive integer n, assume that for all i ∈ Icc 1 (n - 1),
choose n i congruent to 0 module p, then n = p ^ multiplicity p n.
Also see eq_pow_multiplicity_of_choose_modEq_zero_nat for the version with MOD.
- Defined in
- Mathlib.Data.Nat.Choose.Lucas
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 112 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.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- mul_oneproof · cited by 3,885
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- Nat.cast_zeroproof · cited by 1,870
- pow_oneproof · cited by 894
- Nat.choosestatement and proof · cited by 494
- Finset.Iccstatement and proof · cited by 348
- Fact.outproof · cited by 328
- pow_addproof · cited by 315
- Int.ModEqstatement and proof · cited by 147
- multiplicitystatement and proof · cited by 117
Cited by1
Results whose statement or proof uses this declaration.
- Choose.eq_pow_multiplicity_of_choose_modEq_zero_natproof · cited by 2