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This is a very elementary doubt.

Is it true that, $\phi(n)$ the smallest number for which $a^{\phi(n)} \equiv 1 \pmod n$, where $\gcd(a,n)=1$.

  • 3
    No. Consider $a=1$.2012-03-04
  • 3
    No, see [Carmichael function](http://en.wikipedia.org/wiki/Carmichael_function)2012-03-04

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