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Unformatted text preview: k 1 , k 2 , , k n be given integers. For each of the n ! permutations a = H a 1 , a 2 , , a n L of 1, 2, , n , let S H a L = i = 1 n k i a i . Prove that there are two permutations b and c , b c , such that n ! is a divisor of S H b L S H c L . http://imo.wolfram.com/ Problem 5 In a triangle ABC , let AP bisect BAC , with P on BC , and let BQ bisect ABC , with Q on CA . It is known that BAC = 60 and that AB + BP = AQ + QB . What are the possible angles of triangle ABC ? Problem 6 Let a , b , c , d be integers with a > b > c > d > 0. Suppose that a c + b d = H b + d + a c L H b + d a + c L . Prove that a b + c d is not prime. 2 IMO 2001 Competition Problems http://imo.wolfram.com/...
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- Fall '11