Existence of a quadratic polynomial, which represents infinitely many prime numbers
Résumé
No single case of Bunyakovsky's conjecture for degree greater than one has been proved, although numerical evidence in higher degree is consistent with the conjecture. In this paper we overcome such misfortune such misfortune (using Friedlander–Iwaniec theorem, Fermat’s theorem on sums of two squares and Brahmagupta–Fibonacci Identity, Bezout’s lemma and a connection to SL(2, Z) and Hyperbolic Prime Number Theorem).
Mots clés
Landau's problems
Bunyakovsky's conjecture
Complete and subcomplete sequences
Prime numbers
Fermat's theorem on sums of two squares
Dickson's conjecture
Goldbach's conjecture
Bateman-Horn conjecture
Primes represented by polynomials
Sieve theory
Euler’s 6n + 1 theorem
SL2
Brahmagupta–Fibonacci Identity
Friedlander–Iwaniec theorem
n^2+1
Hyperbolic Prime Number Theorem
sl_2
Bezout’s lemma
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