Let
![X](/media/m/9/2/8/92802f174fc4967315c2d8002c426164.png)
be a set of 10,000 integers, none of them is divisible by 47. Prove that there exists a 2007-element subset
![Y](/media/m/3/b/c/3bc24c5af9ce86a9a691643555fc3fd6.png)
of
![X](/media/m/9/2/8/92802f174fc4967315c2d8002c426164.png)
such that
![a - b + c - d + e](/media/m/4/9/2/4929143feb5c009f9f7439a0bf52def0.png)
is not divisible by 47 for any
Author: Gerhard Wöginger, Netherlands
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Let $X$ be a set of 10,000 integers, none of them is divisible by 47. Prove that there exists a 2007-element subset $Y$ of $X$ such that $a - b + c - d + e$ is not divisible by 47 for any $a,b,c,d,e \in Y.$
Author: Gerhard Wöginger, Netherlands