Question 254093
<pre><font size = 4 color = "indigo"><b>
We break {{{8008}}} down into a product of prime factors

{{{8008 = 2*2*2*7*11*13}}}

Every perfect square contains exactly an even number of each
of its prime factors. The product above needs a minimum of one 
more {{{2}}}, one more {{{7}}}, one more {{{11}}}, and one more {{{13}}} to have an 
even number of each of the prime factors 2,7,11,and 13.
That is, it needs to be multiplied by {{{2*7*11*13}}} or {{{2002}}}

Thus if n = {{{2002}}}, we have

{{{8008n = 8008(2002) =  16032016 = 4004^2}}}

Edwin</pre>