关于自然数的黄金平均幂表示
On the representation of the natural numbers by powers of the golden mean
摘要：
在基phi表示中，自然数被写为黄金均值$φ$的幂和。有很多方法可以做到这一点。众所周知的是乔治·伯格曼（George Bergman）于1957年提出的标准表示，其中通过要求表示中不出现连续的幂$φ^n$和$φ^{n+1}$来获得唯一的表示。在本文中，我们引入了一个新的表示，允许权力$φ^0$和$φ^1$可能会出现在同一时间，但没有其他连续的权力。然后，我们认为，这种表示是更接近的经典表示的自然数的幂的整数比伯格曼的标准表示。
英文摘要：
In a base phi representation a natural number is written as a sum of powers of the golden mean $φ$. There are many ways to do this. Well known is the standard representation, introduced by George Bergman in 1957, where a unique representation is obtained by requiring that no consecutive powers $φ^n$ and $φ^{n+1}$ do occur in the representation. In this paper we introduce a new representation by allowing that the powers $φ^0$ and $φ^1$ may occur at the same time, but no other consecutive powers. We then argue that this representation is much closer to the classical representation of the natural numbers by powers of an integer than Bergman's standard representation.
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