Question

If $Y=\{x:x$ is a positive factor of the number $2^{p-1}\left(2^p-1\right)$, where $2^p-1$ is a prime number\}, then $Y$ can be represent in roster form as

• A. $\{2\}$
• B. $\{1,2\}$
• C. $\left\{1,2,2^2,\dots ,2^{p-1}\right\}$
• D. $\left\{1,2,2^2,2^3,\dots ,2^{p-1},\left(2^p-1\right)\right\}$

Answer 1

Answer: (D)

The factors of $2^{p-1}\left(2^p-1\right)$, where $2^p-1$ is a prime number, are $1,2,2^2,2^3,\dots ,2^{p-1}$ and $\left(2^p-1\right)$. So, the given set in roster form is $\left\{1,2,2^2,2^3,\dots ,2^{p-1},\left(2^p-1\right)\right\}$.