Mathematical Enigma - XVII

Algebra Level 5

\(F(x)\) is a fourth order polynomial with integer coefficients and with no common factor. The roots of \(F(x)\) are \(–2, –1, 1, 2\). If \(p\) is a prime number greater than \(97\), then find the largest integer that divides \(F(p)\) for all values of \(p\).

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