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Product Prod^n_{i=1} A_i+k is a power for each n in N

Source: German TST 7, P1, 2009, Exam set by Christian Reiher

July 18, 2009
number theoryprime numbersnumber theory unsolved

Problem Statement

For which n≥2,n∈N n \geq 2, n \in \mathbb{N} are there positive integers A1,A2,…,An A_1, A_2, \ldots, A_n which are not the same pairwise and have the property that the product \prod^n_{i \equal{} 1} (A_i \plus{} k) is a power for each natural number k. k.
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