A quadratic has no root modulo fifty-nine

Proved

WorkbookSource.plus_54193

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

lean-workbooksource-checked

Prove that $x^2 +x +1\equiv 0 (\mod 59 )$ does not have a solution in $Z_{59}$ .

Source: InternLM Lean-Workbook, record lean_workbook_plus_54193 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_54193 (x : ZMod 59) : ¬(x^2 + x + 1 = 0)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_54193; Apache-2.0

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