Mladen Vassilev-Missana and Peter Vassilev

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 14, 2008, Number 3, Pages 11—14

**Download full paper: PDF, 140 Kb**

## Details

### 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

- Dirichlet, P.G.L., R., Dedekind Vorlesungen uber Zahlentheorie. Chelsea, New York, 1968
- Sierpinski, W, What We Know and What We Do Not Know About Prime

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

## Related papers

## Cite this paper

APAVassilev-Missana, M., & Vassilev, P.(2008). Note on polynomials taking infinitely many primes as their values. Notes on Number Theory and Discrete Mathematics, 14(3), 11-14.

ChicagoVassilev-Missana, Mladen, and Peter Vassilev. “Note on Polynomials Taking Infinitely Many Primes as Their Values.” Notes on Number Theory and Discrete Mathematics 14, no. 3 (2008): 11-14.

MLAVassilev-Missana, Mladen, and Peter Vassilev. “Note on Polynomials Taking Infinitely Many Primes as Their Values.” Notes on Number Theory and Discrete Mathematics 14.3 (2008): 11-14. Print.