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PreprintCC BY-NC-ND 4.0arXiv

On some D(u2)-triples and quadruples of triangular numbers

  • Pavao Radić
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Abstract

We classify all D(u2)-triples of triangular numbers whose smallest element is T4u−1 or T4u. We study the regularity of D(N)-triples of triangular numbers. We also show that infinitely many positive integers u admit an all-triangular D(u2)-quadruple. For every positive integer k, triangular number T16k2−1 belongs to infinitely many D(u2)-quadruples of triangular numbers with distinct positive integer parameters u.

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Cite

BibTeXRIS
BibTeX
@misc{radic2026some,
  title = {{On some $D(u^2)$-triples and quadruples of triangular numbers}},
  author = {Pavao Radić},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28018},
  eprint = {2609.28018},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28018},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - On some D(u^2)-triples and quadruples of triangular numbers
AU  - Pavao Radić
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.28018
UR  - https://arxiv.org/abs/2609.28018
AB  - We classify all D(u^2)-triples of triangular numbers whose smallest element is T_4u−1 or T_4u. We study the regularity of D(N)-triples of triangular numbers. We also show that infinitely many positive integers u admit an all-triangular D(u^2)-quadruple. For every positive integer k, triangular number T_16k^2−1 belongs to infinitely many D(u^2)-quadruples of triangular numbers with distinct positive integer parameters u.
ER  -