The number of quadratic residue Pythagorean triples
Inspired by conjectures of Zhi–Wei Sun, we will give an explicit formula for the number of [Formula: see text] such that the elements of the Pythagorean triple [Formula: see text] are all quadratic residues (respectively, quadratic non-residues) where p is an odd prime. Our proof uses explicit evaluation of certain Jacobi sums.
Authors
- Haoyuan Wang (ORCID: https://orcid.org/0009-0008-3584-965X)
- Yan Li (ORCID: https://orcid.org/0000-0002-3134-7715)
Institutions
- University of California, Irvine (US)
- Irvine University (US)
- China Agricultural University (CN)
Publication Details
- Journal
- International Journal of Number Theory
- Published
- 2025-10-08
- DOI
- https://doi.org/10.1142/s1793042126500247
- Primary Topic
- Mathematics and Applications
- Type
- article
- Field-Weighted Citation Impact
- 0.00