IMO Shortlist 1987 problem 7


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2. travnja 2012.
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Given five real numbers u_0, u_1, u_2, u_3, u_4, prove that it is always possible to find five real numbers v0, v_1, v_2, v_3, v_4 that satisfy the following conditions:

(i) u_i-v_i \in \mathbb N, \quad 0 \leq i \leq 4

(ii) \sum_{0 \leq i<j \leq 4} (v_i - v_j)^2 < 4.

Proposed by Netherlands.
Izvor: Međunarodna matematička olimpijada, shortlist 1987