Wolfram Demonstrations Project

12,000+ Open Interactive Demonstrations
Powered by Notebook Technology »

Fundamental Unit

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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

[more]

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 .

[less]

Contributed by: Ed Pegg Jr (June 13)
Open content licensed under CC BY-NC-SA

Details

Snapshots

Embed Code

Take advantage of the Wolfram Notebook Emebedder for the recommended user experience.

Related Demonstrations More by Author
Browse all topics
Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send