Let $k$ be an integer number and $P(X)$ be the polynomial $$P(X) = X^{1997}-X^{1995} +X^2-3kX+3k+1$$Prove that: a) the polynomial has no integer root; β) the numbers $P(n)$ and $P(n) + 3$ are relatively prime, for every integer $n$.
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Tags: algebra, polynomial
Let $k$ be an integer number and $P(X)$ be the polynomial $$P(X) = X^{1997}-X^{1995} +X^2-3kX+3k+1$$Prove that: a) the polynomial has no integer root; β) the numbers $P(n)$ and $P(n) + 3$ are relatively prime, for every integer $n$.