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3 cubes? - not always (Posted on 2012-11-26) Difficulty: 2 of 5
Both 31 and 32 cannot be shown to be a sum of three cubes.
Prove that there is an infinite number of such "twins" (successive integers).

No Solution Yet Submitted by Ady TZIDON    
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Solution Solution Comment 1 of 1

A cube may be {0,1,8}mod3^2.

Hence the sum of 1, 2, or 3 cubes is {0,1,2,3,6,7,8}mod3^2.

In any 9 numbers there will be a successive pair worth {4,5}mod3^2 which cannot be the sum of 3 or less cubes.

 


  Posted by broll on 2012-11-27 00:34:28
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