منابع مشابه
Prime numbers and quadratic polynomials
Some nonconstant polynomials with a finite string of prime values are known; in this paper, some polynomials of this kind are described, starting from Euler’s example (1772) P(x) = x2+x+41: other quadratic polynomials with prime values were studied, and their properties were related to properties of quadratic fields; in this paper, some quadratic polynomials with prime values are described and ...
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Hardy and Littlewood’s Conjecture F implies that the asymptotic density of prime values of the polynomials fA(x) = x 2 + x + A, A ∈ Z, is related to the discriminant ∆ = 1 − 4A of fA(x) via a quantity C(∆). The larger C(∆) is, the higher the asymptotic density of prime values for any quadratic polynomial of discriminant ∆. A technique of Bach allows one to estimate C(∆) accurately for any ∆ < 0...
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The University of Manitoba Sieve Unit is used to find several values of A (> 0) such that the quadratic polynomial x + x + A will have a large asymptotic density of prime values. The Hardy-Littlewood constants which characterize this density are also evaluated.
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We find an explicit expression of the Tutte polynomial of an $n$-fan. We also find a formula of the Tutte polynomial of an $n$-wheel in terms of the Tutte polynomial of $n$-fans. Finally, we give an alternative expression of the Tutte polynomial of an $n$-wheel and then prove the explicit formula for the Tutte polynomial of an $n$-wheel.
متن کاملPrime and Composite Polynomials*
where each <p,(z) is a polynomial of degree greater than unity, prime or composite, we shall say that (2) is a decomposition of F(z). The first result of the present paper is that any two decompositions of a given polynomial into prime polynomials contain the same number of polynomials; the degrees of the polynomials in one decomposition are the same as those in the other, except, perhaps, for ...
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ژورنال
عنوان ژورنال: Revista De La Union Matematica Argentina
سال: 2023
ISSN: ['0041-6932', '1669-9637']
DOI: https://doi.org/10.33044/revuma.2571