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 $a_ib_i$ for $1in$, is there an integer $x$ such that for all $i$, $xa_i(mod \ b_i)$?If both are equivalent why do we require $a_ib_i$ in the problem definition as its equivalent to $a_i<b_i$ ?
A simple Query regarding Modulus Notation?
discrete mathematics
Note that the definition of this problem considers positive integers without $0$, which is instead denoted by $B \bmod B$.