Isolated fraction

Algebra Level 3

If a 1 , a 2 , a 3 , , a n a_1,a_2,a_3,\ldots, a_n are permutation of the set { 1 , 2 , 3 , , n } \{1,2,3,\ldots,n\} , what value can the following expression take?

1 i < j n a j a i j i \large \prod_{1\leq i < j \leq n} \dfrac{a_j-a_i}{j-i}

An irrational number A non-integral rational number An integer

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