论文标题
关于表单$ x^2+c $的数字分解
On the factorization of numbers of the form $X^2+c$
论文作者
论文摘要
我们研究数字的分解$ n = x^2+c $，其中$ c $是固定常数，并且独立于gcd $（x，c）$的值。我们证明了具有算术差$（u_n，z_n）$生成因子化的序列的存在，即：$（u_n）^2+c = z_nz_ {n+1} $。所证明的不同属性使我们能够通过质量数的子集建立新的分解方法并定义蛋白筛。在此基础上提出了一种算法，并导致经验结果，这表明对Landau的第四个问题有积极的答案。
We study the factorization of the numbers $N = X^2+c$, where $c$ is a fixed constant, and this independently of the value of gcd$(X,c)$. We prove the existence of a family of sequences with arithmetic difference $(U_n, Z_n)$ generating factorizations, i.e. such that: $(U_n)^2+c = Z_nZ_{n+1}$. The different properties demonstrated allow us to establish new factorization methods by a subset of prime numbers and to define a prime sieve. An algorithm is presented on this basis and leads to empirical results which suggest a positive answer to Landau's 4th problem.
