lean_workbook_plus_61336

Proved

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

Prove the theorem: Let $a,b,c$ be three integer numbers so that $abc\ne 0$ . Then the equation $ax+by=c$ has at least an integer solution if and only if the greatest common divisor of the numbers $a$ and $b$ divides the number $c$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_61336 (a b c : ℤ) (habc : a * b * c ≠ 0) :  (∃ x y : ℤ, a * x + b * y = c) ↔ (gcd a b) ∣ c   :=  by sorry

Source

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

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