Yifan Zhang and G. Grossman

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 21, 2015, Number 4, Pages 6—16

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## Details

### Authors and affiliations

Yifan Zhang

*Department of Mathematics, Central Michigan University
Mount Pleasant, MI, USA
*

G. Grossman

*Department of of Mathematics, Central Michigan University*

Mount Pleasant, MI, USA

Mount Pleasant, MI, USA

### Abstract

In this paper we consider Diophantine triples {*a, b, c*} (denoted *D(n)*-3-tuples) and give necessary and sufficient conditions for existence of integer *n* given the 3-tuple {*a, b, c*} so that *ab + n, ac + n, bc + n * are all squares of integers. Several examples as applications of the main results, related to both Diophantine triples and quadruples, are given.

### Keywords

- Diophantine triples and quadruples
- Necessary and sufficient conditions

### AMS Classification

- 11D99

### References

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## Cite this paper

APAZhang, I. & Grossman, G. (2015). On Diophantine triples and quadruples, 21(4), 6-16.

ChicagoZhang, Yifan and G. Grossman. “On Diophantine Triples and Quadruples.” Notes on Number Theory and Discrete Mathematics 21, no. 4 (2015): 6-16.

MLAZhang, Yifan and G. Grossman. “On Diophantine Triples and Quadruples.” Notes on Number Theory and Discrete Mathematics 21.4 (2015): 6-16. Print.