# On the problem of Pillai with Tribonacci numbers and powers of 3

Research output: Contribution to journalArticleResearchpeer-review

### Abstract

Let \$ (T_{n})_{n\geq 0} \$ be the sequence of Tribonacci numbers defined by \$ T_0=0 \$, \$ T_1 = T_2=1\$, and \$ T_{n+3}=T_{n+2}+ T_{n+1} +T_n\$ for all \$ n\geq 0 \$. In this note, we find all integers \$ c \$ admitting at least two representations as a difference between a tribonacci number and a power of \$ 3 \$.
Original language English 19.5.6 1-14 14 Journal of Integer Sequences 22 5 Published - 23 Aug 2019

Integer

### Keywords

• Tribonacci sequence
• Pell equation
• Linear forms in logarithms
• Baker's method

### ASJC Scopus subject areas

• Algebra and Number Theory

### Fields of Expertise

• Information, Communication & Computing

### Cite this

In: Journal of Integer Sequences, Vol. 22, No. 5, 19.5.6, 23.08.2019, p. 1-14.

Research output: Contribution to journalArticleResearchpeer-review

@article{b352a3a72853406bacf254654d2bcc6a,
title = "On the problem of Pillai with Tribonacci numbers and powers of 3",
abstract = "Let \$ (T_{n})_{n\geq 0} \$ be the sequence of Tribonacci numbers defined by \$ T_0=0 \$, \$ T_1 = T_2=1\$, and \$ T_{n+3}=T_{n+2}+ T_{n+1} +T_n\$ for all \$ n\geq 0 \$. In this note, we find all integers \$ c \$ admitting at least two representations as a difference between a tribonacci number and a power of \$ 3 \$.",
keywords = "Tribonacci sequence, Pell equation, Linear forms in logarithms, Baker's method",
year = "2019",
month = "8",
day = "23",
language = "English",
volume = "22",
pages = "1--14",
journal = "Journal of Integer Sequences",
issn = "1530-7638",
publisher = "AT & T",
number = "5",

}

TY - JOUR

T1 - On the problem of Pillai with Tribonacci numbers and powers of 3

PY - 2019/8/23

Y1 - 2019/8/23

N2 - Let \$ (T_{n})_{n\geq 0} \$ be the sequence of Tribonacci numbers defined by \$ T_0=0 \$, \$ T_1 = T_2=1\$, and \$ T_{n+3}=T_{n+2}+ T_{n+1} +T_n\$ for all \$ n\geq 0 \$. In this note, we find all integers \$ c \$ admitting at least two representations as a difference between a tribonacci number and a power of \$ 3 \$.

AB - Let \$ (T_{n})_{n\geq 0} \$ be the sequence of Tribonacci numbers defined by \$ T_0=0 \$, \$ T_1 = T_2=1\$, and \$ T_{n+3}=T_{n+2}+ T_{n+1} +T_n\$ for all \$ n\geq 0 \$. In this note, we find all integers \$ c \$ admitting at least two representations as a difference between a tribonacci number and a power of \$ 3 \$.

KW - Tribonacci sequence

KW - Pell equation

KW - Linear forms in logarithms

KW - Baker's method

M3 - Article

VL - 22

SP - 1

EP - 14

JO - Journal of Integer Sequences

JF - Journal of Integer Sequences

SN - 1530-7638

IS - 5

M1 - 19.5.6

ER -