A smaller residue-20 ancestor from divisibility by the thirteenth power of three

Proved

CollatzWork.residueAncestor_of_divisibility

by Sodelin · Sep 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

collatz-work-import

Let $T:\mathbb N\to\mathbb N$ be the shortcut Collatz map: $T(n)=n/2$ for even $n$ and $T(n)=(3n+1)/2$ for odd $n$ . Write $T^k$ for its $k$ -fold iterate, with $T^0(n)=n$ .

Let $r\in\mathbb N$ satisfy $3^{13}\mid(4r+1)$ . Then

\exists m,b\in\mathbb N,\quad 0<m<r,\quad m\equiv20\pmod{27},\quad T^b(m)=r.

The premise is only integer divisibility; a maximal power-of-three factorization is constructed within the proof. The divisor condition remains a genuine guard.

Preamble

import Std
import Init.Grind.Ordered.Module
import Definitions.Def_CollatzWork_ConvergenceStatement
import Definitions.Def_CollatzWork_ResidueAncestorStatement
import Theorems.Thm_CollatzWork_residueAncestor
import Theorems.Thm_CollatzWork_residueAncestor_factor_unit

Formal statement

theorem CollatzWork.residueAncestor_of_divisibility : ResidueAncestorDivisibilityStatement := by sorry

Source

https://github.com/Sodelin/Collatz-Conjecture-Work/blob/026aa4ad4be6453a005ab950b160a9f2204c5271/lean/CollatzWork/ResidueAncestor.lean#L148-L161

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