MathDB
2016-2017 Fall OMO Problem 12

Source:

November 16, 2016
Online Math Open

Problem Statement

For each positive integer n2n\ge 2, define k(n)k\left(n\right) to be the largest integer mm such that (n!)m\left(n!\right)^m divides 2016!2016!. What is the minimum possible value of n+k(n)n+k\left(n\right)?
Proposed by Tristan Shin