Number of Solutions for $p^2 - q^2$ = n? Number of Solutions for $p^2 - q^2 = n$? how do I find it? It was asked in aptitude test of a company , couldn't figure it out. What is the answer of it?

Edit: 

once again i faced similar question for :$p^2 - q^2 = 388$ 

options : 1 , 2 , 3 , More than 3.

what is answer ?
$n = p^2 - q^2 = (p+q)(p-q)$  So every such decomposition gives you a factorization and vice versa.

However there is a gotcha.  If only one of $p+q$ and $p-q$ is odd, then $p$ is not an integer.  So it is the number of factors where the parity of the two factors is the same.

Given the prime factorization of $n$ it is not hard to figure out how many such factorizations exist.
Write the given equation as $p^2-q^2=388$.
Now prime factorize R.H.S.
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