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Challenge 267: Infinite Squares

Dr Reasoner has been working on a problem involving the expression

√(1 + 2/3) x √(1+ 2/4) x √(1 + 2/5) x √(1 + 2/6) x … x √(1 + 2/(n – 1)) x √(1 + 2/n)

[n is an integer, n > 3]

She claims that it is possible to find an integer value for n such that the expression itself is also an integer. She also claims that there are infinitely many values of n that can be chosen to achieve this.

Is Dr Reasoner's first claim true? What about her second claim? Justify your answers clearly.

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