## 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.

ahmedittihad
Posts: 181
Joined: Mon Mar 28, 2016 6:21 pm

### Re: 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
Frankly, my dear, I don't give a damn.