Let p ≡ 5 (mod 8) be a prime. Let h formula presented the class number of the quadratic field Q formula presented. Let T + U formula presented be the fundamental unit of Q(formula presented). It is shown that h(—2p) ≡ h(2p) + 2T+2 (mod 8).

Additional Metadata
Keywords Class number, Dirichlet class number formula, Fundamental unit, Quadratic fields
Persistent URL dx.doi.org/10.1216/RMJ-1981-11-1-19
Journal Rocky Mountain Journal of Mathematics
Citation
Williams, K.S. (1981). The class number of Q(formula presented)MODULO 8, for p ≡ 5 (Mod 8) a prime. Rocky Mountain Journal of Mathematics, 11(1), 19–26. doi:10.1216/RMJ-1981-11-1-19