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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
.
Contributed by:
Ed Pegg Jr
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Fundamental Unit
(
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PERMANENT CITATION
Ed Pegg Jr
"
Fundamental Unit
"
http://demonstrations.wolfram.com/FundamentalUnit/
Wolfram Demonstrations Project
Published: March 17, 2023
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