PreprintCC BY 4.0arXiv
An additive problem in connection with some quadratic real fields with class number one
Abstract
Our aim is to find all the prime numbers p such that p−x2 has at most two different prime factors, for all the odd integers x such that x2<p. We solve entirely the cases p≡ 1,5,7 pmod 8. The case p≡ 3 pmod 8 is solved with one possible exception.
Related
- Ideal class groups of certain real quadratic number fields and factorizations of values of certain quadratic polynomials
- Fermat curves and explicit class field theory for real quadratic number fields
- Finiteness theorems for trace Euclidean quadratic lattices over totally real number fields
- Class numbers and finiteness of norm Euclidean quadratic lattices over algebraic number fields
- Near-quadratic sum-product estimates in fixed number fields
BibTeX
@misc{gica2026additive,
title = {{An additive problem in connection with some quadratic real fields with class number one}},
author = {Alexandru Gica},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16960},
eprint = {2609.16960},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16960},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An additive problem in connection with some quadratic real fields with class number one
AU - Alexandru Gica
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.16960
UR - https://arxiv.org/abs/2609.16960
AB - Our aim is to find all the prime numbers p such that p−x^2 has at most two different prime factors, for all the odd integers x such that x^2<p. We solve entirely the cases p≡ 1,5,7 pmod 8. The case p≡ 3 pmod 8 is solved with one possible exception.
ER -