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Now we know that since n is a natural number, n^2+3n will be a natural number and hence a will be a natural number as well. Therefore the product now is in the form a^2 + 2a clearly (1) short of a perfect square. If p=1, then the sum of the product and p becomes, a^2 + 2a + 1 =
(a+1)^2.
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