Theorems · Theorem · number theory
Nat.self_div_pow_eq_ofDigits_drop
∀ {p : ℕ} (i n : ℕ), 2 ≤ p → n / p ^ i = Nat.ofDigits p (List.drop i (p.digits n))Dividing n by p^i is like truncating the first i digits of n in base p.
- Defined in
- Mathlib.Data.Nat.Digits.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.digitsstatement and proof · cited by 70
- Nat.ofDigitsstatement and proof · cited by 61
- Nat.ofDigits_digitsproof · cited by 15
- Nat.digits_lt_baseproof · cited by 7
- Nat.ofDigits_div_pow_eq_ofDigits_dropproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Nat.sub_one_mul_sum_div_pow_eq_sub_sum_digitsproof · cited by 1