Lean-Workbook Plus 59538: Exact 2-adic valuation of a power sum

Proved

WorkbookRestored.plus_59538

by wamlart · Sep 12, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

lean-workbookrestored-importssource-checked

The largest exponent $e$ for which $2^e$ divides $3^{101}+5^{101}$ is $e=3$ .

Source: Lean-Workbook row lean_workbook_plus_59538 (Apache-2.0). The unchanged proposition comes from the original record; its missing mathematical imports and namespaces are restored here.

Preamble

import Mathlib.NumberTheory.Padics.PadicVal.Defs

Formal statement

theorem WorkbookRestored.plus_59538 :
  padicValNat 2 (3^101 + 5^101) = 3   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_59538; immutable original Prove2Me node 51155ec1-3dda-4c5e-84ce-cf516efd856c

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