Find x, y, and z such that x³+y³+z³=k, for each k from 1 to 100.

below is your answer

Explanation:

There are no solutions whenever k=4,5mod9.

This holds since it is not difficult to verify that for every integer n, we have n3=0,±1mod9.

Up till this year, there were just two values for k in the range 1..100 for which it was not known if there were a solution. These values are k=33,42.

Both values are now known to have solutions. See 42 is the answer to the question “