IMO Shortlist 2007
IMO Shortlist 2007
... present other two constructions for j ≤ 2007, without proof: g j (n) = 1, n < 2007, j, n = 2007, n, n > 2007; h j (n) = max 1, jn 2007 . Also the example for j = 2008 can ... f (2007) ≤ 2008. Now we present a family of examples showing that all values from 1 to 2008 can be realized. Let f j (n) = max{1, n + j 2007} for j = 1, 2, . . . , 2007; f 2008 (n) = n,...
Ngày tải lên: 02/06/2014, 16:36
IMO Shortlist 2004
... ABM. Duˇsan Djuki´c Vladimir Jankovi´c Ivan Mati´c Nikola Petrovi´c IMO Shortlist 2004 From the book The IMO Compendium, www .imo. org.yu Springer Berlin Heidelberg NewYork Hong Kong London Milan ... even. Find all positive integers n such that n has an alternate multiple. 1.1.2 Shortlisted Problems 1. A1 (KOR) IMO4 Let n ≥ 3 be an integer and t 1 , t 2 , . . . , t n positive real nu...
Ngày tải lên: 02/06/2014, 16:34
IMO Shortlist 2006
... by 2 t k , which completes the argument. 47 th International Mathematical Olympiad Slovenia 2006 Shortlisted Problems with Solutions 29 C6. A holey triangle is an upward equilateral triangle of
Ngày tải lên: 02/06/2014, 16:35
IMO Shortlist 2008
... extreme shortage of easy and appr opriate submissions forced the Problem Selection Committee to shortlist a simplified variant. The same one-dimensional Claim is used in both versions. Original ... element of S b is b + 1, a contradiction. 49 th International Mathematical Olympiad Spain 2008 Shortlisted Problems with Solutions Geometry G1. In an acute-angled triangle ABC, point H is the
Ngày tải lên: 02/06/2014, 16:37
IMO Shortlist 2009
... Geometry Problem Shortlist 50th IMO 2009 Geometry G1 BEL (Belgium) Let ABC be a triangle with AB = AC. The angle bisectors ... respectively. Let the triangle XY Z be equilateral. Prove that ABC is equilateral too. 8 50th IMO 2009 Problem Shortlist Geometry G8 BGR (Bulgaria) Let ABCD be a circumscribed quadrilateral. Let g be ... respectively. Show that the orthocenter of I 1 I 2 I 3...
Ngày tải lên: 02/06/2014, 16:41
IMO Shortlist 2010
... 1, j is a TL-block, thus the 51 st International Mathematical Olympiad Astana, Kazakhstan 2010 Shortlisted Problems with Solutions 29 i 1 th row is a n L-row. Now, choosing the ith row to be
Ngày tải lên: 02/06/2014, 16:42
