SAT Math Practice Question #29297 - SATify | SATify

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SAT Math Practice Question #29297 - SATify | SATify

#29297

sequences and series

algebra

binary representation

Recurrence Relations

hard

180 sec

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

$\frac{2 ^{75} + 1}{2 ^{3} + 1} = 2^{a_{1}} + 2^{a_{2}} + \dots + 2^{a_{k}}$ .

What is $k$ ?

A.

35

B.

36

C.

37

D.

38

E.

39