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Let f(x) =a0 + a1x + · · · + amxm, with m ≥ 2 and
am≠ 0, be a polynomial with integer coefficients. Let n be a positive integer,
and suppose that:
i) a2, a3, . . . , am are divisible by all the prime factors of n;
ii) a1 and n are relatively prime.
Prove that...