Theorems · Theorem · number theory
Real.coe_intFib_eq
∀ (n : ℤ), ↑(Int.fib n) = (Real.goldenRatio ^ n - Real.goldenConj ^ n) / √5
Binet's formula for integer values.
- Defined in
- Mathlib.NumberTheory.Real.GoldenRatio
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 137 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Real.sqrtstatement and proof · cited by 545
- Evenproof · cited by 444
- Int.cast_natCastproof · cited by 393
- zpow_natCastproof · cited by 271
- Int.cast_negproof · cited by 224
- mul_powproof · cited by 220
- zpow_negproof · cited by 198
- Nat.fibproof · cited by 74
- neg_one_mulproof · cited by 61
- Int.fibstatement and proof · cited by 26
- Real.goldenRatiostatement and proof · cited by 25
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