Open Access
2012 On $D(-1)$-Quadruples
Nicolae Ciprian Bonciocat, Mihai Cipu, Maurice Mignotte
Publ. Mat. 56(2): 279-304 (2012).


Quadruples $(a,b,c,d)$ of positive integers $a<b<c<d$ with the property that the product of any two of them is one more than a perfect square are studied. Improved lower and upper bounds for the entries $b$ and $c$ are established. As an application of these results, a bound for the number of such quadruples is obtained.


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Nicolae Ciprian Bonciocat. Mihai Cipu. Maurice Mignotte. "On $D(-1)$-Quadruples." Publ. Mat. 56 (2) 279 - 304, 2012.


Published: 2012
First available in Project Euclid: 19 June 2012

zbMATH: 1354.11024
MathSciNet: MR2978325

Primary: 11B37 , 11D09 , 11D45 , 11J68

Keywords: Diophantine $m$-tuples , linear forms in logarithms , Pell equations

Rights: Copyright © 2012 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.56 • No. 2 • 2012
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