If n is a perfect square, then n+ 2 is not a perfect square?
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If n is a perfect square, then n+ 2 is not a perfect square?
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Answer:
n + 2 are perfect square. This means there exist nonnegative integers a; b such that n = a2 and n+2 = b2: Then 2 = (n+ 2) n = b2 a2 = (b a)(b+a): Therefore b+a = 2 and b a = 1, so 2b = 3; and b = 3=2; contradiction with the fact that n is an integer.
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