The word residue is used in a number of different contexts in mathematics. Two of the most common uses are the complex residue of
a pole, and the remainder of a congruence.
The number
in the congruence is called the residue of (mod ).
The residue of large numbers can be computed quickly
using congruences. For example, to find (mod 17), note that
in the congruence 
is called the residue of 
(mod 
).
The residue of large numbers can be computed quickly
using congruences. For example, to find 
(mod 17), note that
