MEMO 2014 pojedinačno problem 4


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24. rujna 2014.
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For integers n \geq k \geq 0 we define the bibinomial coefficient \displaystyle \left(\!\!\binom{n}{k}\!\!\right) by 
    \left(\!\!\binom{n}{k}\!\!\right) = \frac{n!!}{k!!(n - k)!!} \text{.}
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