Theorems · Theorem · number theory
Pell.IsFundamental.eq_pow_of_nonneg
∀ {d : ℤ} {a₁ : Pell.Solution₁ d}, Pell.IsFundamental a₁ → ∀ {a : Pell.Solution₁ d}, 0 < a.x → 0 ≤ a.y → ∃ n, a = a₁ ^ nAny nonnegative solution is a power with nonnegative exponent of a fundamental solution.
- Defined in
- Mathlib.NumberTheory.Pell
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- one_mulproof · cited by 2,841
- mul_commproof · cited by 2,262
- LT.lt.leproof · cited by 2,189
- mul_assocproof · cited by 1,667
- pow_zeroproof · cited by 1,094
- lt_of_not_geproof · cited by 374
- pow_succ'proof · cited by 228
- neg_neg_of_posproof · cited by 227
- LE.le.eq_or_ltproof · cited by 220
- neg_eq_zeroproof · cited by 171
- sub_eq_zero_of_eqproof · cited by 154
- mul_inv_cancelproof · cited by 128
Cited by1
Results whose statement or proof uses this declaration.
- Pell.IsFundamental.eq_zpow_or_neg_zpowproof · cited by 2