A simple Query regarding Modulus Notation? Aren't these two Modulus equations exactly the same (seems obvious): 


$ X = 0 \ (mod\ B) $
$ X = B \ (mod\ B) $


The reason for the query is the following NP Complete Problem from Garey and Jhonson:

AN2, Simultaneous incongruences. 

Given a collection $ [(a_1,b_1),…,(a_n,b_n)]$ of ordered pairs of positive integers with $a_i≤b_i$ for $1≤i≤n$, is there an integer $x$ such that for all $i$, $x≢a_i(mod \ b_i)$?

If both are equivalent why do we require $a_i≤b_i$ in the problem definition as its equivalent to $a_i&lt;b_i$ ?
Note that the definition of this problem considers positive integers without $0$, which is instead denoted by $B \bmod B$.