SAT Math Practice Question #28998 - SATify | SATify

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SAT Math Practice Question #28998 - SATify | SATify

#28998

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

$\frac{2 ^{247} + 1}{2 ^{13} + 1} = 2^{a_{1}} + 2^{a_{2}} + \dots + 2^{a_{k}} .$

What is $k$ ?

A.

116

B.

117

C.

118

D.

119

E.

120