MathNet 2007-part-02 — 187 problems (EN–VI) Question 43

Let $X$ be a set of $10000$ 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 $a, b, c, d, e \in Y$.