Find all natural numbers $(a,b)$ such that
$\frac{b^2+a}{ab-1}$ in an integer.
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
See the link for solution. https://artofproblemsolving.com/community/c6h2023p6413
Frankly, my dear, I don't give a damn.