For a positive integer \(n,\) the equation \[x^{2}=n+y^{2}, \quad x, y \text { integers }\] does not have a solution if and only if \(\qquad\) (a) \(n=2.\) \(\qquad\qquad\) (b) \(n\) is a prime number. \(\qquad\) (c) \(n\) is an odd number. \(\qquad\) (d) \(n\) is an even number not divisible by \(4.\)