$x_{1}^{3}+x_{2}^{3}+\cdots+x_{83}^{3}$

Given that $x_{1};x_{2};\ldots ;x_{83}$ are positive real integers and their product is $83$ .Find the maximum value of the expression above.

The answer is 571869.

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83 is a prime number so only pruced by 1x83. So here we have 82 times 1 to the power of 3 plus 83 to the power of 3. 1^3 remains 1, so:

82x(1)+83^3=571.869