The Diophantine Equation ax6 + by3 + cz2 = 0 in Gaussian In- tegers
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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.
Abstract
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.
참고문헌 (10)
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