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Arithmetic sequence of p terms with product equal to a cube

Source: Baltic Way 2011

November 6, 2011
arithmetic sequencenumber theory proposednumber theory

Problem Statement

Let p≠3p\neq 3 be a prime number. Show that there is a non-constant arithmetic sequence of positive integers x1,x2,…,xpx_1,x_2,\ldots ,x_p such that the product of the terms of the sequence is a cube.
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