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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2015.1
- 수록면
- 587 - 595 (9page)
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In this article, we will examine the Diophantine equation ax6 +by3 +cz2 = 0, for arbitrary rational integers a, b, and c in Gaussian integers and find all the solutions of this equation for many different values of a, b, and c. Moreover, two equations of the type x6 ± iy3 + z2 = 0, and x6 + y3 ± wz2 = 0 are also discussed, where i is the imaginary unit and ! is a third root of unity.
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참고문헌 (10)
참고문헌 신청
E. Lampakis / 2008 / In Gaussian integers, x3 + y3 = z3 has only trivial solutions / Elec. J. Comb. N. T 8 : ~
F. Najman / / Complete classi?cation of torsion of elliptic curves over quadratic cyclo- tomic ?elds / J. Number Theory
F. Najman / / Torsion of elliptic curves over quadratic cyclotomic felds / Math. J. Okayama Univ
F. Najman / 2010 / The diophantine equation x4 § y4 = iz2 in Gaussian integers / Amer. Math. Monthly 117 : 637 ~ 641
H. Cohen / 2007 / Number Theory Volume I: Tools and Diophantine Equations / Graduate Texts in Mathematics (239) : 389 ~
F. Najman / / Complete classi?cation of torsion of elliptic curves over quadratic cyclo- tomic ?elds / J. Number Theory
F. Najman / / Torsion of elliptic curves over quadratic cyclotomic felds / Math. J. Okayama Univ
F. Najman / 2010 / The diophantine equation x4 § y4 = iz2 in Gaussian integers / Amer. Math. Monthly 117 : 637 ~ 641
H. Cohen / 2007 / Number Theory Volume I: Tools and Diophantine Equations / Graduate Texts in Mathematics (239) : 389 ~
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