原文地址:卡廷森林波兰不等式欣赏作者:sqing551.已知 是正数,求证: imo longlist 1967, poland 3 2.已知 是正数,求证 poland finals 1989 3.已知 是正数,求证 这里 , . poland finals 1990 4.已知 是满足 的实数, 求证 when does eq ality occ r? problem 6, polish no 1991 5.已知 是实数,求证 poland, 1992 6.已知 是实数,求证 poland finals 1992 7.已知 是满足 的正数. 是正整数,求证: poland 1993-1994 first ro nd ineq ality 8.已知 , 是不同的实数,且, . 求证 poland finals 1994 9.the positive reals have harmonic mean . find the smallest possible val e of . poland finals 1995 10.已知 是非负数,且 求证: mop poland first ro nd 1995-1996 ineq ality. 1111.已知 是满足 的正数. 求证 poland finals 1996 12.已知 , , 满足: , .求证 poland 1996 ineq ality 13.已知 是实数,求证 poland first ro nd 1998 14.prove that for any real n mbers , , ..., , , , ..., , we have poland finals 1999 15.已知 . 求证: poland 1999 16.已知 . 求证: poland 1999 17.求证 where poland finals 2001 18. are non-negative reals and . prove that at least one of the following ineq alities is tr e: poland finals 2002 19.a real n mber is given. the seq ence is defined by prove that for all positive integers the following ineq ality holds: poland 2002 20.find all positive integers s ch that for all real n mbers the following ineq ality holds: poland second ro nd - poland 2002 21.let be a real n mber. prove that for all finite, strictly increasing seq ences of non-negative integers we have the ineq ality poland finals 2003 22.let real n mbers . prove that . polish mathematical olympiad 2004 final ro nd problem 4 23.已知 求证 poland 2004 24.prove that if the real n mbers lie in the interval , then poland second ro nd - poland 2005 25.positive reals satisfy . prove that: polish second ro nd 2006 26., , , are positive real n mbers satisfying the following  that: poland second ro nd - poland 2007  each cell of a matrix a n mber from a set is written  in the first row n mbers , in the second and so on. exactly of them have been chosen, no two from the same row or the same col mn. let s denote by a n mber chosen from row n mber . show that: poland finals 2008 28.prove for any real nonnegative n mbers : nice ineq ality from kolmogorow s c p [poland ineq ality2008] 29.let be reals. prove the ineq ality poland second ro nd - poland 2009 30.prove thatwhere are positive reals s ch that poland 1st ro nd 20102011 31.let k,m and n be three different positive integers. prove that poland 2013 final ro nd p5 32.if are real n mbers, prove that 1940年春,大约2.2万名波兰军人,知识分子,政界人士和公职人员在卡廷森林遭到苏联军队杀害. 2007年9月21日,安杰伊·瓦依达导演的电影"卡廷惨案"在波兰上映.电影剧本取材于安杰伊·穆拉尔奇克的书"死后检查-卡廷的故事",其中详述了一些被杀害的波兰军官的母亲,妻子,女儿的命运,并重现了卡廷森林惨案的情景.这部电影在2008年获得了奥斯卡最佳外语片奖提名.