If \(a, b,\) and \(c\) are positive integers, is \(c\) a prime number?

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If \(a, b,\) and \(c\) are positive integers, is \(c\) a prime number?

(1) \(a + b = c\)
(2) \(a! + b! = c\)

Answer: E

Source: GMAT Club Tests