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Summary:
The article deals with the identity $$\sum_{i=0}^{n-k}\binom{n-p-1-i}{k-p-1}\cdot\binom{p+i}p = \binom nk$$, where $k, n, p$ are nonnegative integers meeting the condition $p < k \leq n$. The validity of the identity is discussed and the idea of its proof is outlined.
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