lean_workbook_plus_38303

Proved

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

Let $p,q$ be rational numbers. Set $r=p+q\sqrt{7}$ . Prove that there exists intergers $a,b,c,d$ that satisfy: $ad-bc=1$ and $\frac{ar+b}{cr+d}=r$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_38303 (p q : ℚ) (r : ℝ) (hr : r = p + q * Real.sqrt 7) : ∃ a b c d : ℤ, a * d - b * c = 1 ∧ (a * r + b) / (c * r + d) = r   :=  by sorry

Source

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

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