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Bijective integer function

Source: Baltic Way 1992 #12

February 18, 2009
functionlimitalgebra proposedalgebra

Problem Statement

Let N N denote the set of natural numbers. Let ϕ:N→N \phi: N\rightarrow N be a bijective function and assume that there exists a finite limit \lim_{n\rightarrow\infty}\frac{\phi(n)}{n}\equal{}L. What are the possible values of L L?
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