It is given that ( 2 32 + 1 ) is exactly divisible by a certain number. Which of the following is also definitely divisible by the same number?

Q: It is given that ( 2 32 + 1 ) is exactly divisible by a certain number. Which of the following is also definitely divisible by the same number?

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.

( 216 + 1 )
( 216 - 1 )
7 x 213
( 296 + 1 )

Correct Answer: ( 296 + 1 )

Explanation:

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.

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It is given that ( 2 32 + 1 ) is exactly divisible by a certain number. Which of the following is also definitely divisible by the same number?

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