## On the sum of powers of two consecutive Fibonacci numbers.(English)Zbl 1222.11024

Let $$F_n$$ be the Fibonacci numbers, $$s$$ a positive integer. The authors prove that if $$F_n^s+F_{n+1}^s$$ is a Fibonacci number for all suficiently large $$n$$, then $$s=1$$ or $$2$$.

### MSC:

 11B39 Fibonacci and Lucas numbers and polynomials and generalizations

### Keywords:

Fibonacci numbers
Full Text:

### References:

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