A quadratic form of $p = 3k + 1$ primes
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917102106968064 |
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| author | Battseren, Bat-Od Gombodorj, Bayarmagnai |
| author_facet | Battseren, Bat-Od Gombodorj, Bayarmagnai |
| contents | We use Zagier's one-sentence proof approach to show that a prime number $p$ admits a form $p=a^2+ab+b^2$ for some integers $a$ and $b$ if and only if $p=3$ or $p\equiv 1 \pmod{3}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19763 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A quadratic form of $p = 3k + 1$ primes Battseren, Bat-Od Gombodorj, Bayarmagnai Number Theory Group Theory We use Zagier's one-sentence proof approach to show that a prime number $p$ admits a form $p=a^2+ab+b^2$ for some integers $a$ and $b$ if and only if $p=3$ or $p\equiv 1 \pmod{3}$. |
| title | A quadratic form of $p = 3k + 1$ primes |
| topic | Number Theory Group Theory |
| url | https://arxiv.org/abs/2511.19763 |