Q109 / 180 · COMEDK 2024 (Memory Based) · Mathematics

$\left(2^{4 n}-1\right)$ is divisible by

  • A
    8
  • B
    7
  • Correct answer
    C
    15
  • D
    16

Solution

We have, $2^{4 n}-1=16^n-1$
$\therefore a^n-1$ is divisible by $a-1$
$\Rightarrow 16^n-1$ is divisible by $16-1=15$

Hence, the correct answer is option: 'C'.

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