Theorems · Theorem · number theory
Pell.IsFundamental.x_le_x
∀ {d : ℤ} {a₁ : Pell.Solution₁ d}, Pell.IsFundamental a₁ → ∀ {a : Pell.Solution₁ d}, 1 < a.x → a₁.x ≤ a.xThe x-coordinate of a fundamental solution is a lower bound for the x-coordinate
of any positive solution.
- Defined in
- Mathlib.NumberTheory.Pell
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Pell.Solution₁statement and proof · cited by 50
- Pell.Solution₁.xstatement and proof · cited by 42
- Pell.IsFundamentalstatement and proof · cited by 19
Cited by1
Results whose statement or proof uses this declaration.
- Pell.IsFundamental.y_le_yproof · cited by 1