International Matemathic Olimpiad 1998-2003

Berikut ini merupakan soal Olimpiade Matematika Internasional / International Matemathic Olimpiad (IMO) tahun 1998-2003. Silakan anda download pada bagian akhir tulisan.

Example Questions:

A1. In the convex quadrilateral ABCD, the diagonals AC and BD are perpendicular and the opposite sides AB and DC are not parallel. The point P, where the perpendicular bisectors of AB and DC meet, is inside ABCD. Prove that ABCD is cyclic if and only if the triangles ABP and CDP have equal areas.

A2. In a competition there are a contestants and b judges, where b = 3 is an odd integer. Each judge rates each contestant as either “pass” or “fail”. Suppose k is a number such that for any two judges their ratings coincide for at most k contestants. Prove k/a = (b-1)/2b.

A3. For any positive integer n, let d(n) denote the number of positive divisors of n (including 1 and n). Determine all positive integers k such that d(n2) = k d(n) for some n.

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