+479 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 of n are there?
+118677 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 of n are there?
Let the roots be a and b where are and b are positive prime integers.
then
we have (x-a)(x-b) = x^2-(a+b)x +ab
m= a+b
n= ab
which means that m and also n are positive.
So I count 17 possible values of n
