an optimization problem

Anyone can give some hints/references to the following problem? Thanks.

Given N>0, C>0, find v numbers r1,...rv,>0 such that

1. r1+...+rv=N
2. r1^2+...+rv^2>=C
3. r1^3+...+rv^3 is minimum
(Note v is *not* given in the condition)

If N, C, ri are real numbers, what's the solution?

If N, C, ri are integers, what's the solution?

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