Find all positive integers a, b such that each of the equations
$x^2 - ax + b = 0$ and $x^2 - bx + a = 0$
has distinct positive integral roots.
My approach was to use Vieta's formula,
Taking $p, q$ as roots of first equation and $r, s$ as roots of the second equation.
then,
$p + q = a$ and $pq = b$
$r + s = b$ and $rs = a$
Then I'm stumped... I'm unable to proceed after this point.
What do I do after this, or this is completely a wrong method.
Please help me figure this out.
Any help would be appreciated.