@article{Rebot2023,
  author    = {{Petro Kosobutskyy, Dariia Rebot}},
  title     = {{Collatz Conjecture 𝟑𝒏 ± 𝟏 as a Newton Binomial Problem}},
  journal   = {{Computer Design Systems. Theory and Practice}},
  year      = {{2023}},
  volume    = {{5}},
  number    = {{1}},
  pages     = {{9}},
  doi       = {{https://doi.org/10.23939/cds2023.01.137}},
  url       = {{https://science.lpnu.ua/sites/default/files/journal-paper/2023/nov/32226/15.pdf}},
  abstract  = {{The power transformation of Newton's binomial forms two equal 3𝑛 ± 1algorithms
for transformations of numbers n  ℕ, each of which have one infinite cycle with a unit lower limit
of oscillations. It is shown that in the reverse direction, the Kollatz sequence is formed by the lower
limits of the corresponding cycles, and the last element goes to a multiple of three odd numbers. It
was found that for infinite transformation cycles 3n −1 isolated from the main graph with minimum
amplitudes of 5, 7, 17 lower limits of oscillations, additional conditions are fulfilled.
}},
}