SOLUTION: Find the smallest possible integer value of n for which 8008n is a perfect square

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Question 254093: Find the smallest possible integer value of n for which 8008n is a perfect square
Answer by Edwin McCravy(20062) About Me  (Show Source):
You can put this solution on YOUR website!

We break 8008 down into a product of prime factors

8008+=+2%2A2%2A2%2A7%2A11%2A13

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%2A7%2A11%2A13 or 2002

Thus if n = 2002, we have

8008n+=+8008%282002%29+=++16032016+=+4004%5E2

Edwin