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# help

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Suppose the roots of the polynomial $$x^2 - mx + n$$ are positive prime integers (not necessarily distinct). Given that $$m<20$$ how many possible values $$n$$ of are there?

Jan 10, 2019

#1
+3583
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$$\text{the roots are }\\ x = \dfrac{m \pm \sqrt{m^2-4n}}{2}$$

$$\text{as these are integers }m^2 - 4n \text{ must be a perfect square}\\ m<20 \Rightarrow m^2 \leq 19^2 = 361\\ 4n It appears there are indeed 90 valid values of n Jan 10, 2019 ### 1+0 Answers #1 +3583 +2 Best Answer \(\text{the roots are }\\ x = \dfrac{m \pm \sqrt{m^2-4n}}{2}$$

\(\text{as these are integers }m^2 - 4n \text{ must be a perfect square}\\ m<20 \Rightarrow m^2 \leq 19^2 = 361\\ 4n

It appears there are indeed 90 valid values of n

Rom Jan 10, 2019