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On a problem of Pillai with Fibonacci numbers and powers of 3. (English) Zbl 1464.11023

Summary: Consider the sequence \(\{F_n\}_{n \ge 0}\) of Fibonacci numbers defined by \(F_0 = 0, F_1 = 1\), and \(F_{n+2} = F_{n+1} + F_n\) for all \(n \ge 0\). In this paper, we find all integers \(c\) having at least two representations as a difference between a Fibonacci number and a power of 3.

MSC:

11B39 Fibonacci and Lucas numbers and polynomials and generalizations
11J86 Linear forms in logarithms; Baker’s method
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References:

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