Find the greatest exponent $k$ for which $2001^{k}$ divides $2000^{2001^{2002}}+2002^{2001^{2000}}$.
Problem
Source: 13-th Hungary-Israel Binational Mathematical Competition 2002
Tags: number theory proposed, number theory
Source: 13-th Hungary-Israel Binational Mathematical Competition 2002
Tags: number theory proposed, number theory
Find the greatest exponent $k$ for which $2001^{k}$ divides $2000^{2001^{2002}}+2002^{2001^{2000}}$.