Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Disprove the statement "every positive integer is the sum of cubes of 8 non negative integers" May I know how can I disprove it.

As far as concern, 0, 1, 2, 3... is can be obtained using the cubes of 8 non negative integers. eg. 0 = 0 x x 0 .... 8 = 2^3 x 0 x 0 x ...

share|cite|improve this question
Consider $23$.'s_problem – anthus Mar 3 '13 at 7:48
In fact, 23 and 239 are the only integers that actually requires as many as 9 cubes in their representation. – Vincent Tjeng Mar 3 '13 at 7:58
thanks for the answer and the interesting link =) – Jun Hao Mar 3 '13 at 14:29

Removing this from the unanswered list: this is an instance of Waring's problem. In general, 9 cubes are required, rather than 8.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.