Abstract
Let ∈ = ( t + u( d)2/2 be a unit of Q((d)1/2), whose norm = 1. We investigate the properties of the factors of the number u n which is defined by ∈ n = ( t n + u n ( d)1/2)/2. Those properties are applied to the theory of the fundamental unit of Q((d) 1/2). The main result is as follows. Take some unit η = (a + b(d) 1 2 )/2 (>1) whose norm = 1. If the number b satisfies a certain condition, then η = ∈ 0 2 n for some n, where ∈ 0 is the fundamental unit of Q((d) 1/2).
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