$D(4)$-triples with two largest elements in common

Abstract

In this paper we consider two new conjectures concerning $D(4)$-quadruples and prove some special cases which support their validity. The main result is a proof that $\{a,b,c\}$ and $\{a+1,b,c\}$ cannot both be $D(4)$-triples.

arXiv comment11 pages

References in corpus (3)

• There is no Diophantine $D(-1)$--quadruple
• Nonexistence of $D(4)$-quintuples
• Extension of a Diophantine triple with the property $D(4)$