Integer
Posted: Wed Dec 27, 2017 4:17 am
Find all natural numbers $(a,b)$ such that
$\frac{b^2+a}{ab-1}$ in an integer.
$\frac{b^2+a}{ab-1}$ in an integer.
If $ab-1 | b^2+a$ then, $ab-1 | b(b^2+a)-(ab-1)$. So, $ab-1 | b^3+a$. Now this is IMO 1994 P4.
See the link for solution. https://artofproblemsolving.com/community/c6h2023p6413