IMO Shortlist 1968 problem 6


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2. travnja 2012.
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If a_i  \ (i = 1, 2, \ldots, n) are distinct non-zero real numbers, prove that the equation
\frac{a_1}{a_1-x} + \frac{a_2}{a_2-x}+\cdots+\frac{a_n}{a_n-x} = n
has at least n - 1 real roots.
Izvor: Međunarodna matematička olimpijada, shortlist 1968