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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 ...

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    $\begingroup$ Consider $23$. en.wikipedia.org/wiki/Waring's_problem $\endgroup$ – Daniel Pietrobon Mar 3 '13 at 7:48
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    $\begingroup$ In fact, 23 and 239 are the only integers that actually requires as many as 9 cubes in their representation. $\endgroup$ – Vincent Tjeng Mar 3 '13 at 7:58
  • $\begingroup$ thanks for the answer and the interesting link =) $\endgroup$ – Jun Hao Mar 3 '13 at 14:29
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Removing this from the unanswered list: this is an instance of Waring's problem. In general, 9 cubes are required, rather than 8.

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