State which of the following statements is true $2^{16} - 1$ is divisible by

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Solution

The correct option is D 17
2 $^{16} - 1 = {(2^{4})}^{4} - 1 = {(16)}^{4} - 1$
=(16-1)(16+1)(16 $^{2}$ +1)
Hence 2 $^{16}$ -1 is divisible by 17

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State which of the following statements is true 216−1 is divisible by

The correct option is D 17216−1=(24)4−1=(16)4−1=(16-1)(16+1)(162+1)Hence 216-1 is divisible by 17

State which of the following statements is true $2^{16} - 1$ is divisible by

The correct option is D 17
2 $^{16} - 1 = {(2^{4})}^{4} - 1 = {(16)}^{4} - 1$
=(16-1)(16+1)(16 $^{2}$ +1)
Hence 2 $^{16}$ -1 is divisible by 17