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I know few about algebraic number theory but recently I stumbled upon the ring $\mathbb{Z}[\phi]$ where $\phi = \frac{1+\sqrt{5}}{2}$ is the golden ratio. It seems to be a very interesting object to study, so now I'm curious what is known about this ring. Is there some literature about it?

Leif Sabellek
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    What interesting facts do you know about it? I'm not aware of anything that makes it different from other quadratic extensions of $\Bbb Z$, so I'm interested. – rschwieb May 10 '14 at 00:33
  • I am researching about a generalization of fibonacci sequences, taking arbitrary starting values $a,b \in \mathbb{Z}$. I found that mapping such a sequence to the norm of the number $a+b\phi \in \mathbb{Z}$ is an interesing invariant and I think there is a 1-to-1-correspondece between a representing subset of the sequences and the possible values the norm of elements in $\mathbb{Z}[\phi]$ can have. – Leif Sabellek May 10 '14 at 00:44
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    Related: Golden Number Theory – Grigory M May 10 '14 at 23:30
  • I commented about it under one of the answers to the linked question, but I forgot to add a link to the Icosians. – Jyrki Lahtonen Feb 16 '15 at 18:56

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Dodd, Number theory in the quadratic field with golden section unit, Polygonal Pub. House, 1983