A variant of Collatz's conjecture over binary polynomials

• Luis H. Gallardo ^[1] ; Olivier Rahavandrainy ^[1]
  1. [1] Univ. Brest, France
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 69, Nº. 1, 2026, págs. 295-302
• Idioma: inglés
• DOI: 10.33044/revuma.5555
• Enlaces
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• Resumen

  • We study a natural analogue of Collatz's conjecture for polynomials over F2 .

• Referencias bibliográficas
  • G. Alon, A. Behajaina, and E. Paran, On the stopping time of the Collatz map in F2[x], Finite Fields Appl. 99 (2024), Paper No. 102473. DOI...
  • A. Behajaina and E. Paran, The Collatz problem in Fp[x] and Fp[[x]], Finite Fields Appl. 91 (2023), Paper No. 102265. DOI MR Zbl
  • A. Behajaina and E. Paran, The Collatz map analogue in polynomial rings and in completions, Discrete Math. 348 no. 1 (2025), Paper No. 114273....
  • L. H. Gallardo and O. Rahavandrainy, Odd perfect polynomials over F2, J. Théor. Nombres Bordeaux 19 no. 1 (2007), 165–174. DOI MR Zbl
  • L. H. Gallardo and O. Rahavandrainy, Characterization of sporadic perfect polynomials over F2, Funct. Approx. Comment. Math. 55 no. 1 (2016),...
  • L. H. Gallardo and O. Rahavandrainy, On Mersenne polynomials over F2, Finite Fields Appl. 59 (2019), 284–296. DOI MR Zbl
  • K. Hicks, G. L. Mullen, J. L. Yucas, and R. Zavislak, A polynomial analogue of the 3n+1 problem, Amer. Math. Monthly 115 no. 7 (2008),...
  • K. R. Matthews and G. M. Leigh, A generalization of the Syracuse algorithm in Fq[x], J. Number Theory 25 no. 3 (1987), 274–278. DOI MR ...
  • Wikipedia contributors, Collatz conjecture — Wikipedia, the free encyclopedia. Available at https://en.wikipedia.org/wiki/Collatz_conjecture.