Integer

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Katy729
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Joined: Sat May 06, 2017 2:30 am

Integer

Unread post by Katy729 » Wed Dec 27, 2017 4:17 am

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

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

Re: Integer

Unread post by ahmedittihad » Tue Feb 06, 2018 10:01 pm

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.

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