Fundamental Unit

For a squarefree integer , the number is a fundamental unit if . Basically, there are no fractions in either the number or its reciprocal.

For example, the fundamental unit of is . The reciprocal of the fundamental unit is .

For squarefree integers (mod 4), the value is a fundamental unit if . In these cases, is allowed.

Thus, the fundamental unit is either or . Except for the golden ratio, one of the continued fraction convergents of is .

Also, equals one of the values . There are no smaller integers and that give that value for the given .