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Product of elements in two sets is a square

Source: Germany 2007 - Problem 2

December 6, 2022
squaresetProductnumber theory

Problem Statement

Let AA be the set of odd integers ≤2n−1.\leq 2n-1. For a positive integer mm, let B={a+m ∣ a∈A}.B=\{a+m\,|\, a\in A \}. Determine for which positive integers nn there exists a positive integer mm such that the product of all elements in AA and BB is a square.
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