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We address conjectures of P. Erdős and conjectures of Y.-G. Chen concerning the numbers in the title. We obtain a variety of related results, including a new smallest positive integer that is simultaneously a Sierpiński number and a Riesel number and a proof that for every positive integer r, there is an integer k such that the numbers k, k2, k3, . . . , kr(More)
In a recent Monthly note, Saidak [6], improving on a result of Hayes [1], gave Chebyshev-type estimates for the number R(y) = Rf (y) of representations of the monic polynomial f(x) ∈ Z[x] of degree d > 1 as a sum of two irreducible monics g(x) and h(x) ∈ Z[x], with the coefficients of g(x) and h(x) bounded in absolute value by y. Here, we do not distinguish(More)
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