As you now that 03 0 13 1 23 8 33 27 43 64 53 125 so, we have a proof that every positive integer is the sum of the cubes of eight non negative integers. For example 7= 13 + 13 + 13 +13+13+13+ 13 +03 12= 23+ 13 + 13 + 13 +13+03+03+03 Can you disprove this statement?

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Let's try to decompose 23 into the sum:

We need to use more 8 to minimize the number of summands:

$23=8+8+1+1+1+1+1+1+1$

There are nine summands so the statement is false

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Question ID: mtid-5-stid-8-sqid-3115-qpid-1814