Download PDFOpen PDF in browserCurrent versionExistence of a Quadratic Polynomial, Which Represents Infinitely Many Prime Numbers: Bunyakovsky's Conjecture for Degree Greater than One and the 4th Landau ProblemEasyChair Preprint no. 8203, version 36 pages•Date: November 18, 2023AbstractNo 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 (using Friedlander–Iwaniec theorem, Fermat’s theorem on sums of two squares and Brahmagupta–Fibonacci Identity, Bezout’s lemma). Keyphrases: Bunyakovsky’s conjecture, complete and subcomplete sequences, Euler’s 6k + 1 theorem, Fermat’s theorem on sums of two squares, Landau’s problems, prime numbers, primes represented by polynomials, sieve theory
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