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Question

 Let n be a natural number. The number of n's for which (n4 + 2n3 + 2n2 + 2n + 1) is a perfect square is


  1. 2

  2. 1

  3. 7

  4. 0


Solution

The correct option is D

0


For N to be a perfect square, since (n+1)2 is already a perfect square, n2 + 1 must be a perfect square.

But there is no n (natural number) such that n2 + 1 is a perfect square and hence N is a perfect square for no natural number.

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