... 8 2 Solutions2.1 Solutions to the Shortlisted Problems of IMO 2005 1. Clearly, p(x) has to be of the form p(x) = x2+ax±1 where a is an integer.For a = ±1 and ... the same would haveDuˇsan Djuki´c Vladimir Jankovi´cIvan Mati´c Nikola Petrovi´cIMO Shortlist 2005 From the book ”The IMO Compendium”Springerc2006 Springer Scien ce+Business Media, Inc.All ... UzbekistanVIE VietnamYUG Yugoslavia1Problems1.1 The Forty-Sixth IMOM´erida, Mexico, July 8–19, 2005 1.1.1 Contest ProblemsFirst Day (July 13)1. Six points are chosen on the sides of a n equilateral...