A method of finding an integral solution to x3 + y3 = kz4

• Main Authors: Zahari, N. M., Sapar, Siti Hasana, Mohd Atan, Kamel Ariffin
• Format: Conference or Workshop Item
• Language: English
• Published: American Institute of Physics 2010
• Online Access: http://psasir.upm.edu.my/id/eprint/57284/1/A%20method%20of%20finding%20an%20integral%20solution%20to%20x3%20%2B%20y3%20%3D%20kz4.pdf; http://psasir.upm.edu.my/id/eprint/57284/

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.