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PreprintCC BY 4.0arXiv

On concatenations of two k-generalized Pell numbers

  • Cherif B. Deme
  • Kancou D. Fall
  • Khady Faye
  • Bernadette Faye
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Abstract

We study the concatenation of two k-generalized Pell numbers. More precisely, we determine all solutions of the equation Pn(k) = Pm(k) · 10d + Pp(k), where d is the number of decimal digits of Pp(k). We prove that for k ≥ 3 there are no solutions, while for k = 2 the only solution is P4 = 12 = 1|2.

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Cite

BibTeXRIS
BibTeX
@misc{deme2026concatenations,
  title = {{On concatenations of two $k$-generalized Pell numbers}},
  author = {Cherif B. Deme and Kancou D. Fall and Khady Faye and Bernadette Faye},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.15290},
  eprint = {2606.15290},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.15290},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On concatenations of two k-generalized Pell numbers
AU  - Cherif B. Deme
AU  - Kancou D. Fall
AU  - Khady Faye
AU  - Bernadette Faye
PY  - 2026
DA  - 2026/10/11
PB  - arXiv
DO  - 10.48550/arxiv.2606.15290
UR  - https://arxiv.org/abs/2606.15290
AB  - We study the concatenation of two k-generalized Pell numbers. More precisely, we determine all solutions of the equation P_n^(k) = P_m^(k) · 10^d + P_p^(k), where d is the number of decimal digits of P_p^(k). We prove that for k ≥ 3 there are no solutions, while for k = 2 the only solution is P_4 = 12 = 1|2.
ER  -