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The 53rd International Mathematical Olympiad: Problems and Solutions
Problem 3: The guessing game is a game played between two players ( A ) and ( B ). The rules of the game depend on two positive integers ( k ) and ( n ) which are known to both players. At the start of the game the player (...
IMO Shortlist 2011 – Algebra
Algebra A7: Let and be positive real numbers satisfying and Prove that A5: Prove that for every positive integer the set can be partitioned into triples in such a way that the numbers from each triple are the lengths of the sides of some obtuse triangle. A4: Determine all pairs of functions from the set of positive integers to itsels that satisfy for every...
IMO Shortlist 2011 – Number Theory
Number Theory N8: Let and set Prove that is a prime number if and only if the following holds: there is a permutation of the numbers and a sequence of integers such that divides for every where we set N7: Let be an odd prime number. For every integer define the number Let such that Prove that divides N6: Let and be two polynomials with integer coefficients, such that no nonconstant...
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