IMO 1979 LL ROM58

Prove that there exists a natural number k0 such that for

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IMO 1979 LL ROM58

Origin: ROM

Problem

Prove that there exists a natural number k0 such that for every natural number k > k0 we may find a finite number of lines in the plane, not all parallel to one of them, that divide the plane exactly in k regions. Find k0.