On $D(-1)$-Quadruples

Nicolae Ciprian Bonciocat; Mihai Cipu; Maurice Mignotte

doi:pm/1340127807

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Home > Journals > Publ. Mat. > Volume 56 > Issue 2 > Article

2012 On $D(-1)$-Quadruples

Nicolae Ciprian Bonciocat, Mihai Cipu, Maurice Mignotte

Publ. Mat. 56(2): 279-304 (2012).

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Abstract

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.