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Suppose there exists a positive integer n for which is a rational number.
, where p and q positive integers and q ≠ 0.
From (1) and (2),
⇒ n + 1 and n – 1 perfect square of positive integers.
Now, (n + 1) – (n – 1) = 2, which is not possible since any two perfect squares differ by atleast 3.
Hence, there is no positive integer n for which is a rational number.
, where p and q positive integers and q ≠ 0.
From (1) and (2),
⇒ n + 1 and n – 1 perfect square of positive integers.
Now, (n + 1) – (n – 1) = 2, which is not possible since any two perfect squares differ by atleast 3.
Hence, there is no positive integer n for which is a rational number.
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