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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 235.10006

**Autor: ** Erdös, Paul; Graham, Ronald L.

**Title: ** On sums of Fibonacci numbers. (In English)

**Source: ** Fibonacci Q. 10, 249-254 (1972).

**Review: ** A sequence of integers 1 \leq a_{1} \leq a_{2} \leq ... is called complete if every sufficiently large integer n can be written in the form (1) n = **sum** \epsilon_{i}a_{i}, \epsilon_{i} = 0 or 1. The sequence is called strongly complete if it remains complete after omitting any finite number of terms. Let M = (m_{1},m_{2}, ...) be a sequence of non-negative integers. S_{M} is a sequence which contains precisely m_{k} entries equal to F_{k} where F_{k} is the k-th term of the Fibonacci sequence. Put \tau = (1+\sqrt 5)/2. The authors prove that if (2) **sum** ^{oo}_{k = 1}m_{k} \tau ^{-k} < oo then S_{M} is not strongly complete but if the series (2) diverges and m_{k} \tau ^{-k} is monotone then it is strongly complete.

**Classif.: ** * 11B39 Special numbers, etc.

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