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P(X) = X^{1997}-X^{1995} +X^2-3kX+3k+1 - 1997 Romania NMO VIΙI p1

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August 13, 2024
algebrapolynomial

Problem Statement

Let kk be an integer number and P(X)P(X) be the polynomial P(X)=X1997−X1995+X2−3kX+3k+1P(X) = X^{1997}-X^{1995} +X^2-3kX+3k+1 Prove that: a) the polynomial has no integer root; β) the numbers P(n)P(n) and P(n)+3P(n) + 3 are relatively prime, for every integer nn.
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