A residue below a Mersenne modulus

Proved

WorkbookSource.problem_34085

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

lean-workbooksource-checked

The integer $2^{16}+1$ has the following residue modulo $2^{31}-1$ :

2^{16}+1\equiv65537\pmod{2^{31}-1}.

Source: InternLM Lean-Workbook, record lean_workbook_34085 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_34085 : 2^16 + 1 ≡ 65537 [MOD 2^31 - 1]  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_34085; Apache-2.0

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