What is a residue of a power?

A residue of a power, in number theory, refers to the remainder left when a power of an integer is divided by a modulus. Specifically, if ( a ) is an integer and ( n ) is a positive integer, then the residue of ( a^n ) modulo ( m ) is the value of ( a^n \mod m ). This concept is crucial in modular arithmetic and has applications in areas such as cryptography and computational number theory.