IMO Shortlist 1975 problem 7


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2. travnja 2012.
1975 shortlist
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Prove that from x + y = 1 \ (x, y \in \mathbb R) it follows that
x^{m+1} \sum_{j=0}^n \binom{m+j}{j} y^j + y^{n+1} \sum_{i=0}^m \binom{n+i}{i} x^i = 1 \qquad (m, n = 0, 1, 2, \ldots ).
Izvor: Međunarodna matematička olimpijada, shortlist 1975