作者myflame (龍隊 紅隊 太陽隊)
看板IMO_Taiwan
標題從雲飄飄轉來的...放在這比較多人看~
時間Fri Sep 12 18:35:31 2003
感謝chaogold提供題目
1. In triangle ABC prove that a + b + c < r_1 + r_2 + r_3 + min {r_1,r_2,r_3}
where r_1 is the exradius opposite a, r_2 is the exradius opposite b and r_3
is the exradius opposite c.
2. How can you arrange numbers from 1 to 2003 in a row so that avg. of any
two numbers doesn't lie between them? E.g. 2003...1002...1 is invalid as
(1+2003)/2=1002
3.Prove that there are infinitely many primes that can be written as the sum
of a prime and a power of two.
4. [x/(y+z)]^(1/2) + [y/(x+z)]^(1/2) + [z/(y+x)]^(1/2) > 2
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