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

			(1)
			(2)
			(3)
			(4)

so

(5)

Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, pp. 55-56, 1993.

CITE THIS AS:

Weisstein, Eric W. "Residue." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Residue.html