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?

HelpBot Aug 6, 2020

#2**+2 **

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

Melody Aug 21, 2020