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Let a_1 < a_2 < \cdots < a_n be pairwise coprime positive integers with a_1 being prime and a_1 \geq n + 2. On the segment I = [0, a_1 a_2 \cdots a_n] of the real line, mark all integers that are divisible by at least one of the numbers a_1, \ldots, a_n. These points split I into a number of smaller segments. Prove that the sum of the swquares of the length of these segments is divisible by a_1.

(Serbia)

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