number theory proposednumber theoryprime factorization
Problem Statement
Given a natural n>1 and its prime fatorization n=p1α1p2α2⋯pkαk, its false derived is defined by f(n)=α1p1α1−1α2p2α2−1...αkpkαk−1. Prove that there exist infinitely many naturals n such that f(n)=f(n−1)+1.