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2020 AMC 10A Problem 21

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2020 AMC 10A Problem 21AMC 10 Step by Step
Name:                             Date: September 13, 2026
Bases & Digits · difficulty 4 of 5 · about 7 min · position P21-25

There exists a unique strictly increasing sequence of nonnegative integers a1<a2<…<aka_1 < a_2 < … < a_k such that 2289+1217+1=2a1+2a2+…+2ak.\frac{2^{289}+1}{2^{17}+1} = 2^{a_1} + 2^{a_2} + … + 2^{a_k}. What is k?k?

  1. A)

    117117

  2. B)

    136136

  3. C)

    137137

  4. D)

    273273

  5. E)

    306306

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