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Product of Consecutive Tribonacci Numbers With Only One Distinct Digit
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Eric F. Bravo and Carlos A. Gómez

Department of Mathematics

Universidad del Valle

Calle 13 No 100 – 00

Cali

Colombia

Florian Luca

School of Mathematics

University of the Witwatersrand

Johannesburg

South Africa

and

Research Group in Algebraic Structures and Applications

King Abdulaziz University

Jeddah

Saudi Arabia

and

Department of Mathematics

University of Ostrava

30 Dubna 22, 701 03

Ostrava 1

Czech Republic

**Abstract:**

Let (*F*_{n})_{n ≥ 0
be the sequence of Fibonacci
numbers. Marques and Togbé proved that if the product
Fn · · ·
Fn+l-1
is a repdigit (i.e., a number with only
distinct digit in its decimal expansion), with at least two digits,
then (l, n) = (1, 10). In this paper, we solve
the same problem with Tribonacci numbers instead of Fibonacci numbers.
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(Concerned with sequences
A010785
A101292.)

Received January 10 2019; revised versions received January 11 2019; August 14 2019.
Published in *Journal of Integer Sequences*,
August 24 2019.

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