Theorems · Theorem · number theory
Pell.IsFundamental.zpow_eq_one_iff
∀ {d : ℤ} {a : Pell.Solution₁ d}, Pell.IsFundamental a → ∀ (n : ℤ), a ^ n = 1 ↔ n = 0The nth power of a fundamental solution is trivial if and only if n = 0.
- Defined in
- Mathlib.NumberTheory.Pell
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- StrictMono.injectiveproof · cited by 94
- zpow_zeroproof · cited by 52
- Pell.Solution₁statement and proof · cited by 50
- Pell.Solution₁.yproof · cited by 40
- Pell.IsFundamentalstatement and proof · cited by 19
- Pell.IsFundamental.y_strictMonoproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Pell.existsUnique_pos_generatorproof · cited by 1