Number Theory
# Euler's Theorem

Mallory discovers many public keys, including the following:

- $n=70441807$, $e=3$
- $n=10645627$, $e=17$
- $n=63339281$, $e=65537$
- $n=24864431$, $e=257$
- $n=89221291$, $e=17$

What number can Mallory discover is the prime factor of one (or more) of these keys, without needing to factor any of them, making use of a vulnerability of RSA?

Knowing which of the following would allow an attacker to efficiently break the RSA encryption?