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\(2^{122} + 4^{62} + 8^{42} + 4^{64} + 2^{130}\) is divisible by which one of the following integers?

Question and options

2122+462+842+464+21302^{122} + 4^{62} + 8^{42} + 4^{64} + 2^{130} is divisible by which one of the following integers?
  1. 3
  2. 5
  3. 7
  4. 11

Answer and explanation

Correct answer: D - 11
All terms are powers of 2: 2^122 + 2^124 + 2^126 + 2^128 + 2^130 = 2^122(1+4+16+64+256) = 2^122 * 341 = 2^122 * 11 * 31, so divisible by 11 (341 is not divisible by 3, 5 or 7).

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