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Show that an expression does not divide another

Source: Indian Postal Coaching 2012 Set 1 #2

September 19, 2013
number theory unsolvednumber theory

Problem Statement

Let a_1, a_2,\cdots ,a_n be positive integers and let aa be an integer greater than 11 and divisible by the product a1a2⋯ana_1a_2\cdots a_n. Prove that an+1+a−1a^{n+1} + a-1 is not divisible by the product (a + a_1 - 1)(a + a_2 - 1) \cdots (a + a_n - 1).
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