The greatest positive integer k, for whi...

The greatest positive integer k, for which `81^(k) + 1` is a factor of the sum `9^(350) + 9^(348) …… 9^(4) + 9^(2) + 1`

A

81

B

85

C

87

D

88

Verified by Experts

The correct Answer is:

D

Sum can be writeen as
`= 81^(@) + 81 + 8a^(2) + …….81^(175)`
`= (81^(176) - 1)/(81 - 1) = ((81^(88) - 1)(81^(88) + 1))/(81 - 1)` `:. K = 88`

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