Theorems · Theorem · commutative algebra
gcd_pow_right_dvd_pow_gcd
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : GCDMonoid α] {a b : α} {k : ℕ}, gcd a (b ^ k) ∣ gcd a b ^ k- Defined in
- Mathlib.Algebra.GCDMonoid.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidWithZeroGCDMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- pow_zeroproof · cited by 1,094
- CommMonoidWithZerostatement and proof · cited by 913
- pow_succ'proof · cited by 228
- Dvd.dvd.transproof · cited by 148
- GCDMonoid.gcdstatement and proof · cited by 143
- GCDMonoidstatement and proof · cited by 96
- Associated.symmproof · cited by 87
- Associated.dvdproof · cited by 38
- mul_dvd_mul_iff_leftproof · cited by 24
- pow_dvd_pow_of_dvdproof · cited by 12
- gcd_eq_zero_iffproof · cited by 3
- gcd_mul_dvd_mul_gcdproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- gcd_pow_left_dvd_pow_gcdproof · cited by 1