It is given that ( 232 + 1 ) is exactly divisible by a

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It is given that ( 2³² + 1 ) is exactly divisible by a certain number. Which of the following is also definitely divisible by the same number ?

1. ( 2¹⁶ + 1 )
2. ( 2¹⁶ - 1 )
3. 7 x 2¹³
4. ( 2⁹⁶ + 1 )

Correct Option: D

Let 2³² = x and let ( 2³² + 1 ) = ( x + 1 )
( 2⁹⁶ + 1 ) = ( x³ + 1 ) = ( x + 1 )( x² -x + 1 )
Which is clearly divisible by n as ( x + 1 ) is divisible by n.