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Non-perfect Cube Root Sum (Posted on 2015-08-14) Difficulty: 3 of 5
Can the sum of two cube roots of positive non-perfect cubes be an integer?

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No Solution Yet Submitted by K Sengupta    
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re: An idea | Comment 2 of 6 |
(In reply to An idea by Jer)

But we can easily get the product of two cube roots of positive non-perfect cubes to be an integer: 12^(1/3) * 18^(1/3) = 6.


The 12 and the 18 of course come from 2*2*3 and 2*3*3 so the product is a perfect cube while the numbers are not. Substitute any two primes or relative primes.

  Posted by Charlie on 2015-08-14 13:28:01
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