AoPS Wiki talk:Problem of the Day/July 22, 2011

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Problem

AoPSWiki:Problem of the Day/July 22, 2011

Solution

If there is only one integer root, if it is in the form $x - y$, and $y$ is a constant, then $y$ must be a factor of $25$, the polynomial's constant term, because of the Factor Theorem. $-1$ and $1$ are not zeros. Going up from there, we see that $5$ is a zero, so our answer is $5$.

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