Determine all possible octuplet(s) (A, B, C, D, P, Q, R, S) of positive integers, with P ≤ Q ≤ R ≤ S, that satisfy this system of equations:
A + B + C + D = 200, and:
A/P2 + B/Q2 + C/R2 + D/S2 = 7.5
Prove that these are the only octuplet(s) that exist.
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