MathDB

Consider

n

cards with marked numbers

1

through

n

. No number have repeted, namely, each number has marked exactly at one card. They are distributed on

n

boxes so that each box contains exactly one card initially. We want to move all the cards into one box all together according to the following instructions The instruction: Choose an integer

k(1\le k\le n)

, and move a card with number

k

to the other box such that sum of the number of the card in that box is multiple of

k

. Find all positive integer

n

so that there exists a way to gather all the cards in one box.
Thanks to @scnwust for correcting wrong translation.

Problem Statement