Each of A and B is a positive integer.
Find the relationship between A and B such that each of the expressions:
x^{2} + A*x + B and x^{2} + A*x + B + 2 is resolvable into factors of the form (x+p)(x+q), for positive integers p and q.
(In reply to
The whole story? by Jer)
I realized I didn't actually show my solution b=(a^2  9)/4 works.
The first quadratic can be rewritten and factored as
x^{2} + A*x + (A^{2}  9)/4 = (x + (A+3)/2)(x + (A3)/2)
and the second as
x^{2} + A*x + (A^{2}  1)/4 = (x + (A+1)/2)(x + (A1)/2)
[Again, since A is odd, those fractions will yield positive integers for p and q.]

Posted by Jer
on 20151022 07:21:33 