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2x+1 is a perfect square but the following x+1 integers are not.

Source: Spain Mathematical Olympiad 2018 P1

March 17, 2018
algebraSpainnumber theory

Problem Statement

Find all positive integers xx such that 2x+12x+1 is a perfect square but none of the integers 2x+2,2x+3,…,3x+22x+2, 2x+3, \ldots, 3x+2 are perfect squares.
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