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Number Theory

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Prime Factorization, True/False II

NUMTH-MAKB7T

Which of the following statements about prime factorization is true?

Select ALL that apply.

A

The number of distinct prime factors of $2^7-1$ is $1$.

B

The number of distinct prime factors of $2^p-1$ is $\ll \frac{p}{\log p}$ where $p$ is a prime.

C

The number of distinct prime factors of $2^{pq}-1$ is at least $2$ where $p$ and $q$ are distinct primes.

D

A prime $p$ always divides $2^p -1$.