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X, A and m：
x_1 + x_2 + .. + x_m = X
a_1 + a_2 + .. + a_m = A
For a given (a_1, a_2, .. a_m), to maximize x_1^a_1 * x_2^a_2 * ... * x_m^a_m, which is Qm(X, (a_1, a_2, .. a_m)).
Question:
When trying to find Qm(X, (a_1, a_2, .. a_m)), is there an existing formula to get Qm(X, (a_1, a_2, .. a_m)), or we need to calculate x_1^a_1 * x_2^a_2 * ... * x_m^a_m for all (x_1, x_2, .. x_m) combinations?
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Project Euler #190: Maximising a weighted product
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X, A and m：
x_1 + x_2 + .. + x_m = X
a_1 + a_2 + .. + a_m = A
For a given (a_1, a_2, .. a_m), to maximize x_1^a_1 * x_2^a_2 * ... * x_m^a_m, which is Qm(X, (a_1, a_2, .. a_m)).
Question:
When trying to find Qm(X, (a_1, a_2, .. a_m)), is there an existing formula to get Qm(X, (a_1, a_2, .. a_m)), or we need to calculate x_1^a_1 * x_2^a_2 * ... * x_m^a_m for all (x_1, x_2, .. x_m) combinations?