<p>The <a href="https://artofproblemsolving.com/wiki/index.php/Polynomial" title="Polynomial">polynomial</a> <img alt="$x^3 - 2004 x^2 + mx + n$" height="16" src="https://latex.artofproblemsolving.com/e/c/7/ec79eb0fd4cdd168927d761290bff83ff5405780.png" width="175" /> has <a href="https://artofproblemsolving.com/wiki/index.php/Integer" title="Integer">integer</a> coefficients and three distinct positive zeros. Exactly one of these is an integer, and it is the sum of the other two. How many values of <img alt="$n$" height="8" src="https://latex.artofproblemsolving.com/1/7/4/174fadd07fd54c9afe288e96558c92e0c1da733a.png" width="10" /> are possible?</p>

Question No: 260

The polynomial $x^3 - 2004 x^2 + mx + n$ has integer coefficients and three distinct positive zeros. Exactly one of these is an integer, and it is the sum of the other two. How many values of $n$ are possible?

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Tags: Algebra Probability

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