# On Repdigits as Sums of Fibonacci and Tribonacci Numbers

## Abstract

**:**

## 1. Introduction

**Remark**

**1.**

**Theorem**

**1.**

## 2. Auxiliary Results

**Lemma**

**1.**

**Lemma**

**2.**

- $\mathrm{h}\left(xy\right)\le \mathrm{h}\left(x\right)+\mathrm{h}\left(y\right)$;
- $\mathrm{h}(x+y)\le \mathrm{h}\left(x\right)+\mathrm{h}\left(y\right)+log2$;
- $\mathrm{h}\left({\alpha}^{r}\right)=\left|r\right|\xb7\mathrm{h}\left(\alpha \right)$, for all $r\in \mathbb{Q}$.

**Lemma**

**3.**

## 3. The Proof of Theorem 1

#### 3.1. Finding an Upper Bound for n and ℓ

#### 3.2. Reducing the Bound

## 4. Conclusions

## Funding

## Conflicts of Interest

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Trojovský, P.
On Repdigits as Sums of Fibonacci and Tribonacci Numbers. *Symmetry* **2020**, *12*, 1774.
https://doi.org/10.3390/sym12111774

**AMA Style**

Trojovský P.
On Repdigits as Sums of Fibonacci and Tribonacci Numbers. *Symmetry*. 2020; 12(11):1774.
https://doi.org/10.3390/sym12111774

**Chicago/Turabian Style**

Trojovský, Pavel.
2020. "On Repdigits as Sums of Fibonacci and Tribonacci Numbers" *Symmetry* 12, no. 11: 1774.
https://doi.org/10.3390/sym12111774