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 .


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