Factoring one less than a power of two

Proved

WorkbookSource.problem_25121

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

lean-workbooksource-checked

Note that $1023=2^{10}-1\implies1023=(2^5-1)(2^5+1)=31\times33$

Source: InternLM Lean-Workbook, record lean_workbook_25121 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_25121 :
  1023 = (2^5 - 1) * (2^5 + 1)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_25121; Apache-2.0

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