@article{Simons2007,
  author    = {{John L. Simons}},
  title     = {{A simple (inductive) proof for  the non-existence of $2$-cycles for the $3x+1$ problem}},
  journal   = {{J. Number Theory}},
  year      = {{2007}},
  volume    = {{123}},
  pages     = {{10-17}},
}