If \(p, m,\) and \(n\) are positive integers, \(n\) is odd, and \(p = m^2 + n^2,\) is \(m\) divisible by \(4?\)

(1) When \(p\) is divided by \(8,\) the remainder is \(5.\)
(2) \(m - n = 3\)

Answer: A

Source: Veritas Prep