We show that the quartic Diophantine equations $ax^4+by^4=cz^2$ has only trivial solution in the Gaussian integers
for some particular choices of $a,b$ and $c$. Our strategy is by elliptic curves method. In fact, we exhibit
two null-rank corresponding families of elliptic curves over Gaussian field. We also determine the torsion groups of both families.
Diophantine equation elliptic curves quartic equation number of solutions of Diophantine equations
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Makaleler |
Yazarlar | |
Yayımlanma Tarihi | 17 Ocak 2022 |
Yayımlandığı Sayı | Yıl 2022 Cilt: 31 Sayı: 31 |