You program your computer to randomly choose $1001$ distinct natural numbers $\{$ni in N : i in

$\{1,2,...,1001\}=[1,1001]\}$ and then to display the list of all elements of the set D $=\{|$ni $$nj

$|$ :

i$,$ j in $[1,1001],$ i $,$ j$\}.$ You notice that the set D contains a number divisible by $1000.$ Use the

Pigeonhole Principle to check if this is just a coincidence or something unavoidable.