Kantaphon Kuhapatanakul, Pornpawee Anantakitpaisal, Chanokchon Onsri and Suriya Na nhongkai

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 22, 2016, Number 4, Pages 78—81

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## Details

### Authors and affiliations

Kantaphon Kuhapatanakul

*Department of Mathematics, Faculty of Science, Kasetsart University
Bangkok, Thailand*

Pornpawee Anantakitpaisal

*Department of Mathematics, Faculty of Science, Kasetsart University
Bangkok, Thailand*

Chanokchon Onsri

*Department of Mathematics, Faculty of Science, Kasetsart University
Bangkok, Thailand*

Suriya Na nhongkai

*Department of Mathematics, Faculty of Science, Kasetsart University
Bangkok, Thailand*

### Abstract

In this short note, we discuss the integer part for the inverse of 1 − Π_{k=n}^{∞}(1 − 1/*T _{k}*), where

*T*are the Tribonacci numbers. We also consider a similar formula for the Tribonacci numbers with indices in arithmetic progression and give an open problem of the Diophantine equation about the Tribonacci numbers.

_{n}### Keywords

- Tribonacci number
- Infinite product
- Diophantine equation

### AMS Classification

- 11B39
- 11D99

### References

- Anantakitpaisal, P., & Kuhapatanakul, K. (2016) Reciprocal sums of the Tribonacci numbers, J. Integer Seq., 19(2016), Article 16.2.1.
- Ohtsuka, H. (2015) Solution H-734 “Integer Parts of Reciprocals of Tails of Infinite Products with Fibonacci Numbers”, The Fibonacci Quarterly, 53(1), 89.
- N. J. A. Sloane, The On-line Encyclopedia of Integer Sequences, published electronically at http://oeis.org

## Related papers

## Cite this paper

APAKuhapatanakul, K., Anantakitpaisal, P., Onsri, C. & Na nhongkai, S. (2016). Infinite product involves the Tribonacci numbers, Notes on Number Theory and Discrete Mathematics, 22(4), 78-81.

ChicagoKuhapatanakul, Kantaphon, Pornpawee Anantakitpaisal, Chanokchon Onsri and Suriya Na nhongkai “Infinite Product Involves the Tribonacci Numbers.” Notes on Number Theory and Discrete Mathematics 22, no. 4 (2016): 78-81.

MLAKuhapatanakul, Kantaphon, Pornpawee Anantakitpaisal, Chanokchon Onsri and Suriya Na nhongkai, “Infinite Product Involves the Tribonacci Numbers.” Notes on Number Theory and Discrete Mathematics 22.4 (2016): 78-81. Print.