The answer is 4.
The cubes mod9 are {-1,0,1}, but 346^346 mod9 = 4.
Therefore 346^346 cannot be the sum of less than 4 cubes.
Apparently, the largest number that cannot be expressed as the sum of 4 positive cubes has no more than 13 digits. https://mathworld.wolfram.com/CubicNumber.html
Even assuming this is out by an order of magnitude, 346^346 has almost 900 digits.
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Posted by broll
on 2021-03-13 20:12:38 |
Possible Solution
