MEMO 2014 pojedinačno problem 4

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24. rujna 2014.
For integers $n \geq k \geq 0$ we define the bibinomial coefficient $\displaystyle \left(\!\!\binom{n}{k}\!\!\right)$ by Determine all pairs $(n, k)$ of integers with $n \geq k \geq 0$ such that the corresponding bibinomial coefficient is an integer.
Remark. The double factorial $n!!$ is defined to be the product of all even positive integers up to $n$ if $n$ is even and the product of all odd positive integers up to $n$ if $n$ is odd. So e.g. $0!! = 1$, $4!! = 2 \cdot 4 = 8$, and $7!! = 1 \cdot 3 \cdot 5 \cdot 7 = 105$.
Izvor: Srednjoeuropska matematička olimpijada 2014, pojedinačno natjecanje, problem 4