A method of finding an integral solution to x3 + y3 = kz4 - Zahari, N. M.; Sapar, Siti Hasana; Mohd Atan, Kamel Ariffin (American Institute of Physics, 2010)
In this article, we proved that an integral solution (a, b, c) to the equation x3+y3 = kz4 is of the form a = rs, b = rt for any two integers s, t and c =  (r3u/d3)1/4 for some u with (k,r) = d where k divides a3 + b3 and r is a common factor of a and b.