Nonexistence of D(4)-quintuples

JOURNAL OF NUMBER THEORY

卷:194

Article

Bliznac Trebjesanin, Marija¹  Filipin, Alan² 

[1] Univ Split, Fac Sci, Rudera Boskovica 33, Split 21000, Croatia

[2] Univ Zagreb, Fac Civil Engn, Fra Andrije Kacica Miosica 26, Zagreb 10000, Croatia

关键词: Diophantine m-tuples;    Pell equations;    Reduction method;    Linear form in logarithms;   

DOI  :  10.1016/j.jnt.2018.07.013

来源: Elsevier

【 摘 要 】

In this paper we prove a conjecture that a 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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free