Note on polynomials taking infinitely many primes as their values

Mladen Vassilev-Missana and Peter Vassilev
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 14, 2008, Number 3, Pages 11–14
Full paper (PDF, 140 Kb)

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Authors and affiliations

Mladen Vassilev-Missana
5 V. Hugo Str., 1124- Sofia, Bulgaria

Peter Vassilev
CLBME – Bulg. Academy of Sci.

Abstract

In the paper, the polynomials with integer coefficients are considered and a hypothetical sufficient condition for these polynomials to take infinitely many primes as their values is proposed. That provides an alternative equivalent variant of the famous Dirichlet’s theorem for infinitely many primes in arithmetic progressions. Also an interesting analogy between the behaviour of polynomial’s zeros and the integers for which the polynomial takes prime values is noted.

References

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   Numbers. (in Bulgarian), Tehnika, Sofia, 1967, pp. 74-75.
3. Weisstein, Eric W. “Schinzel’s Hypothesis.” From MathWorld – A Wolfram Web Resource. http://mathworld.wolfram.com/SchinzelsHypothesis.html
4. Weisstein, Eric W. “Fundamental Theorem of Algebra.” From MathWorld{A Wolfram Web Resource. http://mathworld.wolfram.com/FundamentalTheoremofAlgebra.html