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A functional ineq

Source: Indian IMOTC 2004 Practice test 2 Problem 4

September 23, 2005
functionarithmetic sequencenumber theory solvednumber theoryBritishMathematicalOlympiad

Problem Statement

Let ff be a bijection of the set of all natural numbers on to itself. Prove that there exists positive integers a<a+d<a+2da < a+d < a+ 2d such that f(a)<f(a+d)<f(a+2d)f(a) < f(a+d) <f(a+2d)
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