## Integer

For discussing Olympiad Level Number Theory problems
Katy729
Posts: 47
Joined: Sat May 06, 2017 2:30 am

### Integer

Find all natural numbers $(a,b)$ such that
$\frac{b^2+a}{ab-1}$ 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.