Show that if f(x)= anxn + an−1xn−1 + ⋯ + α1x + a0, where n ≥ 1 and the coefficients are integers, then there is a positive integer y such that f(y) is composite. (Hint: Assume that f(x)= p is prime, and show that p divides f(x + kp) for all integers k. Conclude that there is an integer y such that f(y) is composite from the fact that a polynomial of degree n, n > 1, takes on each value at most n times.)
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