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تسجيل مستخدم جديدPrime Values of Quadratic Polynomials
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تأليف
N.A. Carella
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This note investigates the prime values of the polynomial $f(t)=qt^2+a$ for any fixed pair of relatively prime integers $ ageq 1$ and $ qgeq 1$ of opposite parity. For a large number $xgeq1$, an asymptotic result of the form $sum_{nleq x^{1/2},, n text{ odd}}Lambda(qn^2+a)gg qx^{1/2}/2varphi(q)$ is achieved for $qll (log x)^b$, where $ bgeq 0 $ is a constant.
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A recent construction by Amarra, Devillers and Praeger of block designs with specific parameters depends on certain quadratic polynomials, with integer coefficients, taking prime power values. The Bunyakovsky Conjecture, if true, would imply that eac
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