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In this paper, we give an explicit lower bound for the class number of real quadratic field , where is a square-free integer, using which is the number of odd prime divisors of .

international journal of mathematics and mathematical sciences

Lower Bound for the Class Number of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>ℚ</mml:mi><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:msqrt><mml:mrow><mml:msup><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:msqrt></mml:mrow></mml:mfenced></mml:mrow></mml:math>

Lower Bound for the Class Number of ℚn2+4