What does 1 modulo p mean? For example, from Gallian's text:
Sylow Test for Nonsimplicity 
Let $n$ be a positive integer that is not prime, and let $p$ be a prime divisor of $n$. If 1 is the only divisor of $n$ that is equal to 1 modulo p, then there does not exist a simple group of order $n$.
I of course understand what some a mod b is (ex. 19 mod 10 = 9); but wouldn't 1 mod anything positive be 1 [edit: changed from 0]? 

1 mod anything greater than 1 will be 1.
