Öz
Kaynakça
- 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
Öz
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This article was retracted on January 03, 2022.
Anahtar Kelimeler
Kaynakça
- 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).
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Yazılım Mühendisliği (Diğer) |
| Bölüm | Articles |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Aralık 2020 |
| Kabul Tarihi | 25 Kasım 2020 |
| Yayımlandığı Sayı | Yıl 2020 Cilt: 2 Sayı: 2 |
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