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Prove: If f(x) = anx^n + an−1x^n−1 + ··· + a1x + a0 has integer coefficients...

Prove: If f(x) = anx^n + an−1x^n−1 + ··· + a1x + a0 has integer coefficients with an ? 0 ? a0 and there are relatively prime integers p, q ∈ Z with f ? p ? = 0, then p | a0 and q | an . [Hint: Clear denominators.]

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I have written a detailed solution to the problem, basically you have to use the fact that p and q are coprime then you can arrive at the conclusion by a simple arrangement. Please find the attachment. If you like my work please give an upvote, also feel free to share your feedback about the solution, this will help me a lot to improve the quality of my answers. Thank you.

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