I am interested in a classic problem of representation of integers as a sum of four cubes of integers. This problem has been partially solved missing only integers of the form 9k ± 4. I got a proof that this is true for rational. This is not important really because it is not given in a ring but in a field (where the operability is easier). From this the following question:
Prove that all rational integer n is a sum of four cubes of nonzero rational numbers.