Arithmetic Function - Multiplicative and Additive Functions

Multiplicative and Additive Functions

An arithmetic function a is

  • completely additive if a(mn) = a(m) + a(n) for all natural numbers m and n;
  • completely multiplicative if a(mn) = a(m)a(n) for all natural numbers m and n;

Two whole numbers m and n are called coprime if their greatest common divisor is 1; i.e., if there is no prime number that divides both of them.

Then an arithmetic function a is

  • additive if a(mn) = a(m) + a(n) for all coprime natural numbers m and n;
  • multiplicative if a(mn) = a(m)a(n) for all coprime natural numbers m and n.

Read more about this topic:  Arithmetic Function

Famous quotes containing the word functions:

    “Mark the babe
    Not long accustomed to this breathing world;
    One that hath barely learned to shape a smile,
    Though yet irrational of soul, to grasp
    With tiny finger—to let fall a tear;
    And, as the heavy cloud of sleep dissolves,
    To stretch his limbs, bemocking, as might seem,
    The outward functions of intelligent man.”
    —William Wordsworth (1770–1850)