Title of article :
A Conjecture on a Symmetric Diagonal Diophantine Equation of Degree Six
Author/Authors :
Jalali, A Urmia University , Janfada, A.S Urmia University , Shabani-Solt, H Urmia University
Abstract :
In this paper, we conjecture that the symmetric di-
agonal Diophantine equation x6 + ky3 + k0z3 = u6 + kv3 + k0w3
has innitely many nontrivial solutions for all rational numbers
k and k0. This conjecture is proved for certain cases.
Keywords :
elliptic curves , Counting solutions of Diophantine equations
Journal title :
Journal of Mathematical Extension(IJME)
