A new family of imaginary quadratic fields with class number divisible by 5

초록

Let Ds be the integer such that 5Ds = F10s+5 where F10s+5 is the 10s + 5th number in Fibonacci sequence. In this paper, we prove that the class number of Q(√−Ds) is divisible by 5 when s≡ 0(mod 20). This gives another remaining infinite family of Fibonacci numbers that can be obtained by the Kishi’s method in (J Number Theory 128, 2450–2458, 2008).

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