Theorems · Theorem · number theory
Int.ModEq.pow_eq_pow
∀ {p x y : ℕ}, Nat.Prime p → p - 1 ∣ x - y → y ≤ x → 0 < y → ∀ (n : ℤ), n ^ x ≡ n ^ y [ZMOD ↑p]- Defined in
- Mathlib.FieldTheory.Finite.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- one_mulproof · cited by 2,841
- Nat.Primestatement and proof · cited by 2,059
- LT.lt.ne'proof · cited by 1,417
- LT.lt.trans_leproof · cited by 678
- one_powproof · cited by 521
- zero_powproof · cited by 361
- pow_mulproof · cited by 210
- Int.ModEqstatement and proof · cited by 147
- Nat.prime_iff_prime_intproof · cited by 27
- IsCoprime.symmproof · cited by 22
- Int.ModEq.symmproof · cited by 13
- Int.ModEq.reflproof · cited by 5
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