D(4)-Triples with Two Largest Elements in Common

Author:

Trebješanin Marija Bliznac1

Affiliation:

1. University of Split , Faculty of Science , Ruđera Boškovića 33 21000 Split , Split , CROATIA

Abstract

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

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Reference16 articles.

1. [1] ADEDJI, K. N.—FILIPIN, A.—TOGBÉ, A: The problem of the extension of D(4)-triple {1, b, c}, Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 26 (2022), 21–43.

2. [2] BAĆIĆ, L.—FILIPIN, A.: On the extensibility of D(4)-pair {k – 2, k + 2}, J. Comb. Number Theory 5 (2013), 181–197.

3. [3] BLIZNAC TREBJEŠANIN, M.: Extension of a Diophantine triple with the property D(4), Acta Math. Hungar. 163 (2021), 213–246.

4. [4] BLIZNAC TREBJEŠANIN, M.—FILIPIN, A.: Nonexistence of D(4)-quintuples, J. Number Theory 194 (2019), 170–217.

5. [5] BONCIOCAT, N. C.—CIPU, M.—MIGNOTTE, M.: There is no Diophantine D(−1)-quadruple, J. Lond. Math. Soc. 105 (2022), 63–99.

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