MathDB

Ben picks a positive number

n

less than

2017

uniformly at random. Then Rex, starting with the number

1

, repeatedly multiplies his number by

n

and then finds the remainder when dividing by

2017

. Rex does this until he gets back to the number

1

. What is the probability that, during this process, Rex reaches every positive number less than

2017

before returning back to

1

Problem Statement