@article{Simons2005,
  author    = {{John L. Simons}},
  title     = {{On the non-existence of $2$-cycles for the $3x+1$ problem}},
  journal   = {{Math. Comp.}},
  year      = {{2005}},
  volume    = {{74}},
  pages     = {{1565--1572}},
  note      = {{MR2137019(2005k:11050)}},
}