Displaying similar documents to “Finiteness of a class of Rabinowitsch polynomials”

Generalizing a theorem of Schur

Lenny Jones (2014)

Czechoslovak Mathematical Journal

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In a letter written to Landau in 1935, Schur stated that for any integer t > 2 , there are primes p 1 < p 2 < ⋯ < p t such that p 1 + p 2 > p t . In this note, we use the Prime Number Theorem and extend Schur’s result to show that for any integers t ≥ k ≥ 1 and real ϵ > 0 , there exist primes p 1 < p 2 < ⋯ < p t such that p 1 + p 2 + ⋯ + p k > ( k - ϵ ) p t .

On prime values of reducible quadratic polynomials

W. Narkiewicz, T. Pezda (2002)

Colloquium Mathematicae

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It is shown that Dickson’s Conjecture about primes in linear polynomials implies that if f is a reducible quadratic polynomial with integral coefficients and non-zero discriminant then for every r there exists an integer N r such that the polynomial f ( X ) / N r represents at least r distinct primes.