2
$\begingroup$

Let $C$ be an abelian additive group and write e for a generator of $C$. The elements of $C$ are then $0,e,2e,3e,\dots,(n-1)e$. If $C$ is finite, prove that the element $ke$ is another generator of $C$ if and only if $k$ and $n$ are relatively prime.

  • 1
    Can you argue the 'if' and/or the 'only if' part?2012-11-12
  • 0
    I do not believe so.2012-11-12

2 Answers 2