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Let f(x) =a[SUB]0[/SUB] + a[SUB]1[/SUB]x + · · · + a[SUB]m[/SUB]x[SUP]m[/SUP], with m ≥ 2 and
am≠ 0, be a polynomial with integer coefficients. Let n be a positive integer,
and suppose that:
i) a[SUB]2[/SUB], a[SUB]3[/SUB], . . . , a[SUB]m[/SUB] are divisible by all the prime factors of n;
ii) a[SUB]1[/SUB] and n are relatively prime.
Prove that for any positive integer k, there exists a positive integer c such
that f(c) is divisible by n[SUP]k[/SUP].
Let f(x) =a[SUB]0[/SUB] + a[SUB]1[/SUB]x + · · · + a[SUB]m[/SUB]x[SUP]m[/SUP], with m ≥ 2 and
am≠ 0, be a polynomial with integer coefficients. Let n be a positive integer,
and suppose that:
i) a[SUB]2[/SUB], a[SUB]3[/SUB], . . . , a[SUB]m[/SUB] are divisible by all the prime factors of n;
ii) a[SUB]1[/SUB] and n are relatively prime.
Prove that for any positive integer k, there exists a positive integer c such
that f(c) is divisible by n[SUP]k[/SUP].
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