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2

Part of 2010 China Second Round Olympiad

Problems(1)

2010 China Second Round,test 2,problem 2

Source:

2/11/2012
Given a fixed integer k>0,r=k+0.5k>0,r=k+0.5,define f1(r)=f(r)=r[r],fl(r)=f(flāˆ’1(r))(l>1)f^1(r)=f(r)=r[r],f^l(r)=f(f^{l-1}(r))(l>1) where [x][x] denotes the smallest integer not less than xx. prove that there exists integer mm such that fm(r)f^m(r) is an integer.
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