# On a problem of Pillai with Fibonacci numbers and powers of 3

Research output: Contribution to journalArticleResearchpeer-review

### Abstract

Consider the sequence \$ \{F_{n}\}_{n\geq 0} \$ of Fibonacci numbers defined by \$ F_0=0 \$, \$ F_1 =1\$ and \$ F_{n+2}=F_{n+1}+ F_{n} \$ for all \$ n\geq 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 \$.
Original language English 1-15 15 Boletín de la Sociedad Matemática Mexicana https://doi.org/10.1007/s40590-019-00263-1 E-pub ahead of print - 17 Sep 2019

Lame number
Integer

### Keywords

• Fibonacci number
• Linear forms in logarithms
• Baker's method

### ASJC Scopus subject areas

• Algebra and Number Theory

### Cite this

In: Boletín de la Sociedad Matemática Mexicana, 17.09.2019, p. 1-15.

Research output: Contribution to journalArticleResearchpeer-review

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