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Question

The greatest divisor of (a−b)(a+b)(a2+b2)(a4+b4)(a8+b8)(a16+b16) is

A
a16b16
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B
a16+b16
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C
a31b31
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D
a32b32
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Solution

The correct option is D a32b32
(ab)(a+b)(a2+b2)(a4+b4)(a8+b8)(a16+b16)
Using the formula,a2b2=(a+b)(ab)
=(a2b2)(a2+b2)(a4+b4)(a8+b8)(a16+b16)
=(a4b4)(a4+b4)(a8+b8)(a16+b16)
=(a8b8)(a8+b8)(a16+b16)
=(a16b16)(a16+b16)
=(a32b32)

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