### Abstract

Original language | English |
---|---|

Article number | 19.5.6 |

Pages (from-to) | 1-14 |

Number of pages | 14 |

Journal | Journal of Integer Sequences |

Volume | 22 |

Issue number | 5 |

Publication status | Published - 23 Aug 2019 |

### Fingerprint

### 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

*Journal of Integer Sequences*,

*22*(5), 1-14. [19.5.6].

**On the problem of Pillai with Tribonacci numbers and powers of $3$.** / Ddamulira, Mahadi.

Research output: Contribution to journal › Article › Research › peer-review

*Journal of Integer Sequences*, vol. 22, no. 5, 19.5.6, pp. 1-14.

}

TY - JOUR

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

AU - Ddamulira, Mahadi

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 -