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IMO Shortlist 1969 problem 15

1969 shortlist tb
(CZS 4) Let K_1,\cdots , K_n be nonnegative integers. Prove that K_1!K_2!\cdots K_n! \ge \left[\frac{K}{n}\right]!^n, where K = K_1 + \cdots + K_n

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