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edited Apr 13, 2017 at 12:58

Mark Sapir's point is of course valid. The equation $x^2 + y^2 = 2z^2$ is a different matter. There was a discussion of this previously on Math Overflow: see Arithmetic Progressions of Squares Arithmetic Progressions of Squares

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created May 22, 2012 at 14:15

Ben Green

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Mark Sapir's point is of course valid. The equation $x^2 + y^2 = 2z^2$ is a different matter. There was a discussion of this previously on Math Overflow: see Arithmetic Progressions of Squares