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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2024 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Construction of diagonal quintic threefolds with infinitely many rational points
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by Maciej Ulas;
Math. Comp. 93 (2024), 2503-2511
DOI: https://doi.org/10.1090/mcom/3953
Published electronically: February 14, 2024

Abstract:

In this note we present a construction of an infinite family of diagonal quintic threefolds defined over $\mathbb {Q}$ each containing infinitely many rational points. As an application, we prove that there are infinitely many quadruples $B=(B_{0}, B_{1}, B_{2}, B_{3})$ of co-prime integers such that for a suitable chosen integer $b$ (depending on $B$), the equation $B_{0}X_{0}^5+B_{1}X_{1}^5+B_{2}X_{2}^5+B_{3}X_{3}^{5}=b$ has infinitely many positive integer solutions.
References
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Bibliographic Information
  • Maciej Ulas
  • Affiliation: Institute of Mathematics, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland
  • MR Author ID: 764558
  • ORCID: 0000-0002-1927-4453
  • Email: maciej.ulas@uj.edu.pl
  • Received by editor(s): October 3, 2023
  • Received by editor(s) in revised form: November 30, 2023, December 13, 2023, and January 17, 2024
  • Published electronically: February 14, 2024
  • © Copyright 2024 American Mathematical Society
  • Journal: Math. Comp. 93 (2024), 2503-2511
  • MSC (2020): Primary 11D41, 13P15
  • DOI: https://doi.org/10.1090/mcom/3953
  • MathSciNet review: 4759382