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PreprintCC0arXiv

A Short Proof of a Theorem of Pan and Zhang

  • Xiangyu Wang
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Abstract

Pan and Zhang proved that a positive proportion of positive integers can be represented in the form a2+b2+2c2, where (a,b,c) are nonnegative integers. In this note, we give a short proof of their result. The proof uses Romanoff's method and an elementary divisor argument to control the relevant second moment.

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Cite

BibTeXRIS
BibTeX
@misc{wang2026short,
  title = {{A Short Proof of a Theorem of Pan and Zhang}},
  author = {Xiangyu Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.37508},
  eprint = {2609.37508},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.37508},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - A Short Proof of a Theorem of Pan and Zhang
AU  - Xiangyu Wang
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2609.37508
UR  - https://arxiv.org/abs/2609.37508
AB  - Pan and Zhang proved that a positive proportion of positive integers can be represented in the form a^2+b^2+2^c^2, where (a,b,c) are nonnegative integers. In this note, we give a short proof of their result. The proof uses Romanoff's method and an elementary divisor argument to control the relevant second moment.
ER  -