SAT Math Practice Question #28997 - SATify | SATify

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SAT Math Practice Question #28997 - SATify | SATify

#28997

algebra

exponents

binary representation

hard

120 sec

There exists a unique strictly increasing sequence of nonnegative integers $a_{1} < a_{2} < \dots < a_{k}$ such that

$\frac{2 ^{165} + 1}{2 ^{11} + 1} = 2^{a_{1}} + 2^{a_{2}} + \dots + 2^{a_{k}} .$

What is $k$ ?

A.

76

B.

77

C.

78

D.

79

E.

80