Let \(a_1\le a_2\le \cdots \le a_n\) be integers. Prove that
\(\displaystyle\prod_{1\le j<i\le n} \frac{a_i-a_j}{i-j}\)
is an integer.
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Let \(a_1\le a_2\le \cdots \le a_n\) be integers. Prove that
is an integer.