A Reduction of Integer Factorization to Modular Tetration

Abstract

Let [Formula: see text]. By [Formula: see text] and [Formula: see text], we denote the [Formula: see text] th iterate of the exponential function [Formula: see text] evaluated at [Formula: see text], also known as tetration. We demonstrate how an algorithm for evaluating tetration modulo natural numbers [Formula: see text] could be used to compute the prime factorization of [Formula: see text] and provide heuristic arguments for the efficiency of this reduction. Additionally, we prove that the problem of computing the squarefree part of integers is deterministically polynomial-time reducible to modular tetration.