Fundamental unit (number theory)
From Wikipedia, the free encyclopedia
In algebraic number theory, a fundamental unit is a generator for the torsion-free unit group of the ring of integers of a number field, when that group is infinite cyclic. See also Dirichlet's unit theorem.
For rings of the form , the fundamental unit has the form where (x,y) is the smallest nontrivial solution to Pell's equation x2 - ny2 = 1 or x2 - ny2 = -1. (For example, if n is a prime that is 1 mod 4 then the fundamental unit comes from a solution of the second equation.)
This number theory-related article is a stub. You can help Wikipedia by expanding it. |