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China Team Selection Test 2014 TST 1 Day 1 Q3

Source: China Nanjing , 12 Mar 2014

March 12, 2014
functionalgebrapolynomialnumber theory proposednumber theoryChina TST

Problem Statement

Let the function f:N∗→N∗f:N^*\to N^* such that (1) (f(m),f(n))≤(m,n)2014,∀m,n∈N∗(f(m),f(n))\le (m,n)^{2014} , \forall m,n\in N^*; (2) n≤f(n)≤n+2014,∀n∈N∗n\le f(n)\le n+2014 , \forall n\in N^* Show that: there exists the positive integers NN such that f(n)=n f(n)=n , for each integer n≥Nn \ge N. (High School Affiliated to Nanjing Normal University )
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