A floor and fractional-part equation has no positive solution

Proved

WorkbookSource.problem_2274

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Prove that there's no real positive solutions for $x + 2022 = \lfloor x \rfloor \cdot \{ x \}$

Source: InternLM Lean-Workbook, record lean_workbook_2274 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_2274 (x : ℝ) (hx : 0 < x): ¬ (x + 2022 = Int.floor x * (x - Int.floor x))  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_2274; Apache-2.0

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