Research Article
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Year 2020, , 79 - 89, 30.12.2020
https://doi.org/10.47086/pims.827611

Abstract

References

  • S. D. Hoehner, The Hasse-Minkowski Theorem in Two and Three Variables(2012). etd.ohiolink.edu/!etd.sendfile?accession=osu1338317481
  • G. A. Jones and J. M. Jones, Elementary Number Theory(Springer, 1998).
  • W. J. LeVeque, Fundamentals of Number Theory(Dover Publications, 1977).

Retracted: The Hasse-Minkowski Theorem and Legendre's Theorem for Quadratic Forms in Two and Three Variables

Year 2020, , 79 - 89, 30.12.2020
https://doi.org/10.47086/pims.827611

Abstract

Determining the solvability of equations has been an extended and fundamental study in Mathematics. The local-global principle states two objects are equivalent globally if and only if they are equivalent locally at all places. By applying this principle, the Hasse - Minkowski theorem is able to identify the existence of rational solutions of an equation. This paper explores the applications of the Hasse-Minkowski theorem to homogeneous quadratic forms in two and three variables. After providing some of the necessary proofs and definitions, we have been able to introduce some complete computer programs implementing the Hasse-Minkowski theorems and Legendre theorem with some supporting functions like the Eratosthenes sieve.


This article was retracted on January 03, 2022. 

References

  • S. D. Hoehner, The Hasse-Minkowski Theorem in Two and Three Variables(2012). etd.ohiolink.edu/!etd.sendfile?accession=osu1338317481
  • G. A. Jones and J. M. Jones, Elementary Number Theory(Springer, 1998).
  • W. J. LeVeque, Fundamentals of Number Theory(Dover Publications, 1977).
There are 3 citations in total.

Details

Primary Language English
Subjects Software Engineering (Other)
Journal Section Articles
Authors

Phuc Ngo 0000-0002-9658-4877

Mehmet Dik 0000-0003-0643-2771

Publication Date December 30, 2020
Acceptance Date November 25, 2020
Published in Issue Year 2020

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