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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