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\sqrt{n + 1} + \sqrt{n - 1} is rational for non natural n

Source: 2001 Moldova JBMO TST p5

February 20, 2021
number theoryrational

Problem Statement

Determine if there is a non-natural natural number nn with the property that n+1+n−1\sqrt{n + 1} + \sqrt{n - 1} is rational.
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