@ARTICLE{Janfada,
author = {Shabani-Solt., H. and Yusefnejad, N. and Janfada, A. S. and },
title = {On the Diophantine Equation x^6+ky^3=z^6+kw^3},
volume = {15},
number = {1},
abstract ={Given the positive integers m,n, solving the well known symmetric Diophantine equation xm+kyn=zm+kwn, where k is a rational number, is a challenge. By computer calculations, we show that for all integers k from 1 to 500, the Diophantine equation x6+ky3=z6+kw3 has infinitely many nontrivial (y≠w) rational solutions. Clearly, the same result holds for positive integers k whose cube-free part is not greater than 500. We exhibit a collection of (probably infinitely many) rational numbers k for which this Diophantine equation is satisfied. Finally, appealing these observations, we conjecture that the above result is true for all rational numbers k. },
URL = {http://ijmsi.ir/article-1-1004-en.html},
eprint = {http://ijmsi.ir/article-1-1004-en.pdf},
journal = {Iranian Journal of Mathematical Sciences and Informatics},
doi = {10.29252/ijmsi.15.1.15},
year = {2020}
}