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P(x) = x^{n + 1} + kx^n - 870x^2 + 1945x + 1995

Source: Vietnam TST 1995, Problem 2

July 27, 2008
algebrapolynomialmodular arithmeticsearchRational Root Theoremalgebra unsolved

Problem Statement

Find all integers k k such that for infinitely many integers n≥3 n \ge 3 the polynomial P(x)=xn+1+kxn−870x2+1945x+1995 P(x) =x^{n+ 1}+ kx^n - 870x^2 + 1945x + 1995 can be reduced into two polynomials with integer coefficients.
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