Let f(x) \equal{} x^8 \plus{} 4x^6 \plus{} 2x^4 \plus{} 28x^2 \plus{} 1. Let p>3 be a prime and suppose there exists an integer z such that p divides f(z). Prove that there exist integers z1,z2,…,z8 such that if g(x) \equal{} (x \minus{} z_1)(x \minus{} z_2) \cdot \ldots \cdot (x \minus{} z_8), then all coefficients of f(x) \minus{} g(x) are divisible by p. algebrapolynomialnumber theorycoefficientsDivisibilityIMO Shortlist