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Thread: Another Phi Proof

  1. #1
    Super Member
    Feb 2008

    Another Phi Proof

    Let & denote the phi function

    Show that, for any given m, the equation &(n) = m has finitely many solutions n (or no solutions)
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  2. #2
    Super Member PaulRS's Avatar
    Oct 2007
    It follows from this post that there's a finite number of positive integers $\displaystyle n$ such that $\displaystyle \phi(n)\leq m$ (1) (since $\displaystyle \phi(n)\to +\infty$ as $\displaystyle n\to +\infty$ ), hence your equation must have a finite number of solutions -since it's a subset of the integers that satisfy (1) -.
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