Problem

Source: American Mathematical Monthly

Tags: function, induction, strong induction, algebra proposed, algebra



Given a positive integer number k, define the function f on the set of all positive integer numbers to itself by f(n)={1,if nk+1f(f(n1))+f(nf(n1)),if n>k+1 Show that the preimage of every positive integer number under f is a finite non-empty set of consecutive positive integers.