Theorems · Theorem · commutative algebra
Finset.exists_eq_pow_of_mul_eq_pow_of_coprime
∀ {ι : Type u_2} {R : Type u_3} [inst : CommSemiring R] [GCDMonoid R] [Subsingleton Rˣ] {n : ℕ} {c : R} {s : Finset ι}
{f : ι → R}, (∀ i ∈ s, ∀ j ∈ s, i ≠ j → IsCoprime (f i) (f j)) → ∏ i ∈ s, f i = c ^ n → ∀ i ∈ s, ∃ d, f i = d ^ n- Defined in
- Mathlib.RingTheory.IntegralDomain
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- CommSemiringstatement and proof · cited by 10,911
- Unitsstatement and proof · cited by 2,804
- Finset.prodstatement and proof · cited by 2,356
- Finset.eraseproof · cited by 455
- IsCoprimestatement and proof · cited by 321
- Finset.prod_insertproof · cited by 109
- GCDMonoidstatement and proof · cited by 96
- Finset.insert_eraseproof · cited by 65
- Finset.notMem_eraseproof · cited by 59
- Finset.erase_subsetproof · cited by 31
- IsCoprime.prod_rightproof · cited by 4
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