Carmichael

Carmichael is a surname of Scottish origin and a toponym. The name derives from Carmichael, a parish and village in South Lanarkshire, Scotland, from which families later emigrated to North America and other regions. The name has since spread worldwide and is borne by numerous individuals and institutions.

Place names bearing Carmichael include Carmichael, California, an unincorporated community and census-designated place in Sacramento County. The name also appears in other countries as townships, streets, or districts, reflecting historical Scottish settlement and migration patterns.

As a surname, Carmichael has been associated with figures in politics, science, literature, and the arts. One notable bearer is Robert Carmichael, a Scottish mathematician known for work in number theory, including Carmichael numbers, which are composite integers that pass Fermat's little theorem test for all bases coprime to the number.

In mathematics, Carmichael numbers are composite integers n such that a^n ≡ a mod n for every integer a; these numbers are named after Robert Carmichael. The Carmichael function, often denoted λ(n), is another concept in number theory linked to Carmichael, describing the exponent of the multiplicative group of integers modulo n.