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Let G(x) be an irreducible polynomial with integer coefficients. It is conjectured that the set {n ∈ N : G(n) is prime} is infinite for most G(x) If Pr denotes the set of squarefree positive integers with at most r prime factors, we consider the set {n ∈ N : G(n) ∈ Pr} with the goal of showing that it is infinite for a suitable choice of r. Considerable work has been done on this problem, with the ... read moremost notable results being due to Iwaniec, Buhˇstab, and Richert. Here we show that if deg(G(x)) = 2, then we may take r = 2.
Original file name: LemkeOliver_ActaArith_Vol151read less
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