MathDB
Partial sum is divisible by n^n

Source: Cono Sur 2003 #6

November 18, 2015
number theorycono sur

Problem Statement

Show that there exists a sequence of positive integers x1,x2,xn,x_1, x_2,…x_n,… that satisfies the following two conditions: (i) Every positive integer appears exactly once, (ii) For every n=1,2,n=1,2,… the partial sum x1+x2++xnx_1+x_2+…+x_n is divisible by nnn^n.