SSC Mock'16 : Problem 1

For discussing Olympiad Level Number Theory problems
Mehedi Hasan Nowshad
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Joined: Sat Jun 13, 2015 1:46 pm
Location: Halishahar, Chittagong

SSC Mock'16 : Problem 1

Unread post by Mehedi Hasan Nowshad » Sat Nov 12, 2016 6:10 pm

Well, this might be easy but still an interesting one to me.

Find all finite sets of positive integers with at least two elements such that for any two numbers $a,b$ belonging to the set with $a>b$, the number $\dfrac{b^2}{a-b}$ belongs to the set, too.
"Failure is simply the opportunity to begin again, this time more intelligently."
- Henry Ford

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