Let $f(x) =x^n-a_1 x^{n-1}+...+(-1)^n a_n \in \mathbb{Z} [X] $. If $-\frac{5}{3}$ is a root of $f$, then $3 |1$. What theorem implies this and what is the general result?
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3This is the rational root Theorem – lulu Mar 02 '19 at 16:29
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RRT = Rational Root Test (onsite link) The Theorem holds in any GCD domain, e.g. any UFD. – Bill Dubuque Mar 02 '19 at 17:05
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Thank you for your help! – MathEnthusiast Mar 02 '19 at 17:15