# Diophantine quadruples and quintuples modulo 4

Andrej Dujella
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 4, 1998, Number 4, Pages 160–164
Full paper (PDF, 2596 Kb)

## Details

### Authors and affiliations

Andrej Dujella
Department of Mathematics, University of Zagreb,
Bijenicka cesta 30, 10000 Zagreb, CROATIA

### Abstract

A Diophantine m-tuple with the property D(n) is a set { a1, a2 , … am} of positive integers such that for 1 ≤ i < jm, the number aiaj + n is a perfect square. In the present paper we give necessary conditions that the elements a1 of a set {a1, a2, a3, a4, a5, a6} must satisfy modulo 4 in order to be a Diophantine quintuple.

### Keywords

• Diophantine m-tuple,
• Pn-set
• congruences

• 11A07
• 11B75
• 11D79

### References

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## Cite this paper

Dujella, A. (1998). Diophantine quadruples and quintuples modulo 4. Notes on Number Theory and Discrete Mathematics, 4(4), 160-164.