If P is prime and both of the equations x2 + px-444p = 0 are integers, then p=______ ．

If P is prime and both of the equations x2 + px-444p = 0 are integers, then p=______ ．

Let two of the original equations X1 and X2, then x1x2 = - 444p, ∵ P are prime numbers, so one of x1x2 is a multiple of P. let X1 = KP (k is an integer), and X1 + x2 = - P, ∵ x2 = - (K + 1) P, ∵ x1x2 = KP [- (K + 1) P] = - K (K + 1) P2 = - 444p, that is, K (K + 1) P = 22.3.37, when k = 3, P = 37, ∵

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