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A Necessary and Sufficient Condition for <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mi>k</mi> <mo>=</mo> <mi mathvariant="normal">ℚ</mi> <mfenced open="(" close=")" separators="|"> <mrow> <msqrt> <mrow> <mn>4</mn> <mi>n</mi> <msup> <mrow> <mtext> </mtext> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>1</mn> </mrow> </msqrt> </mrow> </mfenced> </math> to Have Class Number <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"> <mi>ω</mi> <mfenced open="(" close=")" …
In this paper, we give a necessary and sufficient condition for real quadratic field <math xmlns="http://www.w3.org/1998/Math/MathML" id="M3"> <mi>k</mi> <mo>=</mo> <mi mathvariant="normal">ℚ</mi> <mfenced open="(" close=")" separators="|"> <mrow> <msqrt> <mrow> <mn>4</mn> <mi>n</mi> <msup> <mrow> <mtext> </mtext> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>1</mn> </mrow> </msqrt> </mrow> </mfenced> </math> to have class number …