Fundamental Unit

Author

Eric W. Weisstein
January 27, 2009

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Algebra/FundamentalUnit.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/FundamentalUnit.html.

©2009 Wolfram Research, Inc. except for portions noted otherwise

Enumeration

From Old Package

DeleteCases[{#,FundamentalUnit[#]}&/@Range[100],{_,_FundamentalUnit}]//Simplify//TableForm

Transpose[FundamentalUnitTU/@Select[Range[100],!IntegerQ[Sqrt[#]]&]]

{#,FundamentalUnit[#]}&/@Select[Range[100],!IntegerQ[Sqrt[#]]&]//Simplify//TableForm

NumberFieldFundamentalUnits

f=Flatten/@DeleteCases[{#,NumberFieldFundamentalUnits[(Sqrt[#])]//RootReduce}&/@Range[102],{_,{}}];

l=Length[f]/2

Grid[Flatten/@Transpose[Partition[f,l,l,{1,1},{}]],Dividers->All]//TraditionalForm

d==8

(1/2)(2+(Sqrt[8]))//Simplify

With[{d=8},Reduce[(t^2-d u^2==-4||t^2-d u^2==4)&&0<t<100&&0<u<100,{t,u},Integers]]