On the quadratic subfield of a ๐โ-extension of an imaginary quadratic number field
On the quadratic subfield of a ๐โ-extension of an imaginary quadratic number field
We determine explicitly the quadratic subfield of a noncyclotomic <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper Z 2"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>Z</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">{Z_2}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-extension of an imaginary quadratic number field and get a congruence property of the integer solution of a certain indeterminate equation.