Theorems · Theorem · number theory
Zsqrtd.norm_eq_one_iff_mem_unitary
∀ {d : ℤ} {a : ℤ√d}, a.norm = 1 ↔ a ∈ unitary (ℤ√d)An element of ℤ√d has norm equal to 1 if and only if it is contained in the submonoid
of unitary elements.
- Defined in
- Mathlib.NumberTheory.Zsqrtd.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 43 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Submonoidstatement · cited by 3,086
- Nat.cast_oneproof · cited by 2,501
- Int.cast_oneproof · cited by 371
- unitarystatement · cited by 207
- Zsqrtdstatement and proof · cited by 105
- Zsqrtd.normstatement and proof · cited by 35
- Zsqrtd.norm_eq_mul_conjproof · cited by 5
- Unitary.mem_iff_self_mul_starproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Pell.is_pell_solution_iff_mem_unitaryproof · cited by 1
- Zsqrtd.mker_norm_eq_unitaryproof · cited by 0