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On short products of primes in arithmetic progressions. (arXiv:1705.06087v1 [math.NT])
来源于:arXiv
We give several families of reasonably small integers $k, \ell \ge 1$ and
real positive $\alpha, \beta \le 1$, such that the products $p_1\ldots p_k s$,
where $p_1, \ldots, p_k \le m^\alpha$ are primes and $s \le m^\beta$ is a
product of at most $\ell$ primes, represent all reduced residue classes modulo
$m$. This is a relaxed version of the still open question of P. Erdos, A. M.
Odlyzko and A. Sarkozy (1987), that corresponds to $k = \ell =1$ (that is, to
products of two primes). In particular, we improve recent results of A. Walker
(2016). 查看全文>>