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Theorems · Theorem · number theory

Nat.range_mul_add

∀ (m k : ℕ), (Set.range fun n => m * n + k) = {n | ↑n = ↑k ∧ k ≤ n}

The range of (m * · + k) on natural numbers is the set of elements ≥ k in the residue class of k mod m.

Defined in
Mathlib.Data.ZMod.Basic
Cited by
1 results in Mathlib
Foundations
Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound

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