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The class number of ๐‘„(โˆš-๐‘), for ๐‘ƒโ‰ก1(๐‘š๐‘œ๐‘‘8) a prime

The class number of ๐‘„(โˆš-๐‘), for ๐‘ƒโ‰ก1(๐‘š๐‘œ๐‘‘8) a prime

Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="h left-parenthesis negative p right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>h</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mo>โˆ’<!-- โˆ’ --></mml:mo> <mml:mi>p</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">h( - p)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be the class number of the quadratic field <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper Q left-parenthesis square-root negative p right-parenthesis"> <mml:semantics> <mml:mrow> โ€ฆ