**Kantaphon Kuhapatanakul, Natnicha Meeboomak and Kanyarat Thongsing**

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 24, 2018, Number 3, Pages 56–61

DOI: 10.7546/nntdm.2018.24.3.56-61

**Full paper (PDF, 146 Kb)**

## Details

### Authors and affiliations

**Kantaphon Kuhapatanakul**

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

**Natnicha Meeboomak**

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

**Kanyarat Thongsing**

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

### Abstract

Let be a positive integer. We study the Diophantine equation . This Diophantine equation generalizes a result of Gürel [5] for . We also prove that the product is a perfect square only for the values for which the triangular number is a perfect square.

### Keywords

- Diophantine equation
- Perfect square
- Quartic polynomial
- Quadratic polynomial

### 2010 Mathematics Subject Classification

- 11D25
- 11D09

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## Cite this paper

Kuhapatanakul, K., Meeboomak, N., & Thongsing, K. (2018). On products of quartic polynomials over consecutive indices which are perfect squares. *Notes on Number Theory and Discrete Mathematics*, 24(3), 56-61, DOI: 10.7546/nntdm.2018.24.3.56-61.