The Bunyakovsky conjecture (or Bouniakowsky conjecture) gives a criterion for a polynomial f ( x ) {\displaystyle f(x)} in one variable with integer coefficients...

of Sciences. Bunyakovsky was a mathematician, noted for his work in theoretical mechanics and number theory (see: Bunyakovsky conjecture), and is credited...

any natural number) that each satisfy all three conditions in the Bunyakovsky conjecture, and for any prime p there is an integer x such that the values...

consequence of other number-theoretic conjectures such as the Bunyakovsky conjecture and Bateman–Horn conjecture. One example of near-square primes are...

from 2 2 {\displaystyle 2^{2}} and 3 2 {\displaystyle 3^{2}} . Bunyakovsky conjecture: if an integer-coefficient polynomial f {\displaystyle f} has a...

conjecture Kelvin's conjecture Kouchnirenko's conjecture Mertens conjecture Pólya conjecture, 1919 (1958) Ragsdale conjecture Schoenflies conjecture (disproved...

corresponding polynomial to b is an irreducible polynomial, so if Bunyakovsky conjecture is true, then there are infinitely many bases b such that the corresponding...

Bateman–Horn conjecture, it is a matter of basic importance to understand the case when P has no fixed prime divisor (this has been called Bunyakovsky's property[citation...

values 0, 1, 2, ... This statement is a special case of an earlier conjecture of Bunyakovsky and remains open. Hardy and Littlewood further assert that, asymptotically...

that assumes an infinite number of values that are prime; see Bunyakovsky conjecture. Another prime generator is defined by the recurrence relation a...

polynomials. His 1958 conjecture on the prime values of polynomials, known as Schinzel's hypothesis H, both extends the Bunyakovsky conjecture and broadly generalizes...

simultaneously generate prime values infinitely often is that they satisfy Bunyakovsky's property, that there does not exist a prime number p that divides their...

the representation of a prime number in that base. This is the Bunyakovsky conjecture and its truth or falsity remains an open question. Eisenstein's...

infinitely many centered k-gonal numbers which are primes (assuming the Bunyakovsky conjecture). Since all centered octagonal numbers are also square numbers,...

builds on the earlier Bunyakovsky conjecture, for a single polynomial, and on the Hardy–Littlewood conjectures and Dickson's conjecture for multiple linear...

Bunsen, German inventor – Bunsen burner Viktor Bunyakovsky, Russian mathematician – Bunyakovsky conjecture Johan Burgers Dutch businessman — Royal Burgers'...

that Φ n ( b ) {\displaystyle \Phi _{n}(b)} is prime. In fact, Bunyakovsky conjecture implies that, for every n, there are infinitely many b > 1 such...

of the form 4 n + 3 {\displaystyle 4n+3} (Silverman 2013). The Bunyakovsky conjecture generalizes Dirichlet's theorem to higher-degree polynomials. Whether...

grandfather, Viktor Bunyakovsky, was also a noted mathematician who worked in number theory, specifically with the Bunyakovsky conjecture and the Cauchy–Schwarz...

quantum mechanics Vladimir Berkovich, developed Berkovich spaces Viktor Bunyakovsky, noted for his work in theoretical mechanics and number theory, and is...