Prime-generating quadratic polynomials
DOI:
https://doi.org/10.33044/revuma.2571Abstract
Let $a,b,c$ be integers. We provide a necessary condition for the function $|ax^2 + bx + c|$ to generate only primes for consecutive integers. We then apply this criterion to give sufficient conditions for the real quadratic field $\mathcal{K}=\mathbb{Q}(\sqrt{d})$, $d\in\mathbb{N}$, to have class number one, in terms of prime-producing quadratic polynomials.
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