Suppose the roots of the polynomial x2−mx+n are positive prime integers (not necessarily distinct). Given that m<20 how many possible values n of are there?
the roots are x=m±√m2−4n2
\(\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
