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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

Real quadratic fields with class numbers divisible by five


Author: Charles J. Parry
Journal: Math. Comp. 31 (1977), 1019-1029
MSC: Primary 12A25; Secondary 12A50
DOI: https://doi.org/10.1090/S0025-5718-1977-0498483-X
MathSciNet review: 0498483
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Abstract: Conditions are given for a real quadratic field to have class number divisible by five. If 5 does not divide m, then a necessary condition for 5 to divide the class number of the real quadratic field with conductor m or 5m is that 5 divide the class number of a certain cyclic biquadratic field with conductor 5m. Conversely, if 5 divides the class number of the cyclic field, then either one of the quadratic fields has class number divisible by 5 or one of their fundamental units satisfies a certain congruence condition modulo 25.


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DOI: https://doi.org/10.1090/S0025-5718-1977-0498483-X
Article copyright: © Copyright 1977 American Mathematical Society