On the class numbers of the n-th layers in the cyclotomic Z₂-extension of Q(√5)

Let Kₙ be the n-th layer of the cyclotomic Z₂-extension of Q(√5) and h(Kₙ) the class number of Kₙ. In this paper, we claim that if an odd prime number satisfies ≡ 38 or ≡ 58, then does not divide h(Kₙ) for any positive integer n.