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The 9th Balkan Mathematical Olympiad
1992年第9届巴尔干地区数学奥林匹克
  1. Let a(n) = 34n. For which n is (ma(n)+6 - ma(n)+4 - m5 + m3) always divisible by 1992 ?
  2. Prove that (2n2 + 3n + 1)n ≥ 6nn! n! for all positive integers.
  3. ABC is a triangle area 1. Take D on BC, E on CA, F on AB, so that AFDE is cyclic. Prove that : area DEF ≤ EF2/(4 AD2).
  4. For each n > 2 find the smallest f(n) such that any subset of {1, 2, 3, ... , n} with f(n) elements must have three which are relatively prime (in pairs).
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