Nonexistence of $D(4)$-quintuples

Abstract

In this paper we prove a conjecture that $D(4)$-quintuple does not exist using both classical and new methods. Also, we give a new version of the Rickert's theorem that can be applied on some $D(4)$-quadruples.

38 pages; some mistakes corrected, some explanations added

References in corpus (1)

• The extension of some D(4)-pairs

Cited by in corpus (8)

• D(n)-quintuples with square elements
• Diophantine quadruples with the properties $D(n_1)$ and $D(n_2)$
• Extension of a Diophantine triple with the property $D(4)$
• A Polynomial Variant of Diophantine Triples in Linear Recurrences
• On the largest element in D(n)-quadruples
• Improved upper bounds on Diophantine tuples with the property $D(n)$
• On Diophantine triples containing a triangular number
• $D(4)$-triples with two largest elements in common