Hi all,

this is a question I've been doing. Let (known) be some composite odd integer. Find two numbers and such that :

- is factorable over the real numbers, with integer coefficients in the standard form and factorized form.

- is factorable over the real numbers, with integer coefficients in the standard form and factorized form.

I've been thinking, for a quadratic equation to satisfy these properties, its discriminant must be positive and be a perfect square. Let and denote the discriminants of equations one and two. We have :

And I also noted that , and this could be useful regarding the difference of two squares.

And so, if I could find the values of and , I could easily work out and with a simple system of equations. But what I've done beyond this point does not lead to anything interesting, so I'm wondering, do I have enough information about the discriminants to work them out ?

Does anyone have any idea to put me on the right track again ? Thanks all