On long $\kappa$-tuples with few prime factors
Abstract
We prove that there are infinitely many integers n such that the total number of prime factors of $(n + h_1) \cdots (n + h_\kappa)$ is exactly $(1 + o(1))\kappa\log\kappa$. Our result even ensures us that these prime factors are fairly evenly distributed among every factors $n + h_i$.
Domains
Number Theory [math.NT]| Origin | Files produced by the author(s) |
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