MathDB
2010 China Second Round,test 2,problem 2

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February 11, 2012
modular arithmeticnumber theory proposednumber theory

Problem Statement

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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