Primes of the form \pm a^2\pm qb^2

zbMATH Open1382.11033arXiv1207.0172MaRDI QIDQ5172348

Eugen J. Ionasçu, Jeff Patterson

Publication date: 16 February 2015

Abstract: Representations of primes by simple quadratic forms, such as $pm{a}^{2}pmq{b}^2$, is a subject that goes back to Fermat, Lagrange, Legendre, Euler, Gauss and many others. We are interested in a comprehensive list of such results, for $qle20$. Some of the results can be established with elementary methods and we put them at work on some instances. We are introducing new relationships between various representations.

Full work available at URL: https://arxiv.org/abs/1207.0172

zbMATH Keywords

quadratic reciprocityPigeonhole principle

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) Other number representations (11A67) Primes (11A41)

Related Items (2)

Primes of the form \(\lfloor \alpha p+\beta \rfloor\) ⋮ Primes of the form 2p+1

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