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Found problems: 1

2003 Korea Junior Math Olympiad, 2
Tags: Integer , quadratics equation , algebra , number theory , quadratics
$a, b$ are odd numbers that satisfy $(a-b)^2 \le 8\sqrt {ab}$. For $n=ab$, show that the equation $$x^2-2([\sqrt n]+1)x+n=0$$ has two integral solutions. $[r]$ denotes the biggest integer, not strictly bigger than $r$.