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2018 preRMO p15, 2a-b, a-2b and a+b all distinct squares

Source:

August 7, 2019
minimumnumber theoryPerfect SquaresPerfect Square

Problem Statement

Let aa and bb be natural numbers such that 2a−b2a-b, a−2ba-2b and a+ba+b are all distinct squares. What is the smallest possible value of bb ?
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