Where All Roads Meet: Modular Exponentiation

In addition to the calculational rules for addition, subtraction, and multiplication in residue classes we can also define an operation of exponentiation, where the exponent specifies how many times the base is to be multiplied by itself. Exponentiation is carried out, as usual, by means of recursive calls to multiplication: For a in ℤ _m we have a0:= ī and ae+1 := a · ae.