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:
“When Western people train the mind, the focus is generally on the left hemisphere of the cortex, which is the portion of the brain that is concerned with words and numbers. We enhance the logical, bounded, linear functions of the mind. In the East, exercises of this sort are for the purpose of getting in tune with the unconsciousto get rid of boundaries, not to create them.”
—Edward T. Hall (b. 1914)
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