Incompatible remainder conditions

Proved

WorkbookSource.problem_30423

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

lean-workbooksource-checked

We seek $x<\text{lcm}(3,4,8)=24$ such that $x\equiv0\pmod3$ , $x\equiv0\pmod8$ , and $x ot\equiv0\pmod4$ . There are no values that fit these criteria, so the answer is $\boxed{0}$

Source: InternLM Lean-Workbook, record lean_workbook_30423 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_30423 (x : ℕ) (hx : x < 24) : ¬ (x % 3 = 0 ∧ x % 8 = 0 ∧ x % 4 ≠ 0)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_30423; Apache-2.0

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