$4^{11} + 4^{12} + 4^{13} + 4^{14} + 4^{15}$ is divisible by

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341

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All of the above

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Solution

The correct option is D All of the above
$4^{11} + 4^{12} + 4^{13} + 4^{14} + 4^{15}$
$= 4^{11} (1 + 4^{1} + 4^{2} + 4^{3} + 4^{4}) = 4^{11} \times 341$
The factors of 341 are: 1, 11, 31 and 341. Thus, we can say that the values in each of the three options would divide the expression.

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