lean_workbook_plus_16179

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Let $\gcd(b,c) = g \Rightarrow \gcd(a,g) = 1 \Rightarrow au + gv = 1 \Rightarrow au \equiv 1 \bmod g$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_16179  (a b c g u v : ℕ)
  (h₀ : Nat.gcd b c = g)
  (h₁ : Nat.gcd a g = 1)
  (h₂ : a * u + g * v = 1)
  (h₃ : 0 < g) :
  a * u ≡ 1 [ZMOD g]   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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