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Bunyakovsky conjecture  Wikipedia
https://en.wikipedia.org/wiki/Bunyakovsky_conjecture
The Bunyakovsky conjecture (or Bouniakowsky conjecture) gives a criterion for a polynomial $${\displaystyle f(x)}$$ in one variable with integer coefficients to give infinitely many prime values in the sequence$${\displaystyle f(1),f(2),f(3),\ldots .}$$ It was stated in 1857 by the Russian mathematician Viktor Bunyakovsky. The following three conditions are necessary for $${\displaystyle f…
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(PDF) Proof of Bunyakovsky's conjecture  ResearchGate
https://www.researchgate.net/publication/311081099_Proof_of_Bunyakovsky's_conjecture
In 1857, twenty years after Dirichlet's theorem on arithmetic progressions, the conjecture of the Ukrainian mathematician Victor Y. Bunyakovsky (18041889) is already a try to generalize this ...
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polynomials  Bunyakovsky conjecture  Mathematics Stack ...
https://math.stackexchange.com/questions/370783/bunyakovskyconjecture
Apr 23, 2017 · The Bunyakovsky conjecture states the following : Let $f$ be an irreducible polynomial and $d$ denote the gcd of the set $f(a)$, where $a$ runs over the integers. Then, $f(a)/d$ is prime for infinite many integers $a$.
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Bunyakovskii conjecture  Encyclopedia of Mathematics
https://encyclopediaofmath.org/wiki/Bunyakovskii_conjecture
Bunyakovskii's conjecture is that these conditions are sufficient. A special case of this conjecture is that the polynomial $ x ^ {2} + 1 $ represents infinitely many prime numbers. Similarly, the Dirichlet theorem about infinitely many primes in an arithmetic progression comes from considering the polynomial $ ax + b $ with relatively prime integers $ a > 0 $ and $ b $.
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Proof of Bunyakovsky's Conjecture, viXra.org ePrint ...
https://vixra.org/abs/1611.0390
Nov 01, 2016 · Bunyakovsky's conjecture states that under special conditions, polynomial integer functions of degree greater than one generate innitely many primes. The main contribution of this paper is to introduce a new approach that enables to prove Bunyakovsky's conjecture.
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bunyakovsky conjecture : definition of bunyakovsky ...
http://dictionary.sensagent.com/bunyakovsky%20conjecture/enen/
The Bunyakovsky conjecture (or Bouniakowsky conjecture) stated in 1857 by the Ukrainian mathematician Viktor Bunyakovsky, claims that an irreducible polynomial of degree two or higher with integer coefficients generates for natural arguments either an infinite set of numbers with greatest common divisor exceeding unity, or infinitely many prime numbers.
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(PDF) Proof of Bunyakovsky's conjecture
https://www.researchgate.net/publication/342550406_Proof_of_Bunyakovsky's_conjecture
Jun 30, 2020 · PDF  In 1857, twenty years after Dirichlet’s theorem on arithmetic progressions, the conjecture of the Ukrainian mathematician Victor Y. Bunyakovsky...  Find, …
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On a (possible?) equivalence of Bunyakovsky conjecture
https://mathoverflow.net/questions/226794/onapossibleequivalenceofbunyakovskyconjecture
Whether you prefer to use the label "Bunyakovsky's Conjecture" to mean Conjecture 1 or Conjecture 1+ is a matter of taste; both are equally inaccessible to proof aside from the linear case. Ribenboim and Pollack each consider "Bunyakovsky's Conjecture" to mean Conjecture 1+.
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Sum of two squares and implication of Bunyakovsky conjecture
https://mathoverflow.net/questions/187311/sumoftwosquaresandimplicationofbunyakovskyconjecture
Bunyakovsky's conjecture implies that either $p(x)$ is reducible or the content is not one (i.e. all coefficients have a common prime divisor) or $p(x)$ has a fixed divisor for congruence reasons when the content is one (like $x^2+x+2$, which is always even as pointed out in the comments).
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Bunyakowsky's conjecture is proven? [closed]
https://mfrhtyj.blogspot.com/2019/01/bunyakowskysconjectureisprovenclosed.html
Jan 09, 2019 · Tetramur is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct.
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