On products of primes and almost primes in arithmetic progressions

被引：0
|
作者：
Igor E. Shparlinski
机构：
[1] Macquarie University,Department of Computing
来源：
Periodica Mathematica Hungarica | 2013年 / 67卷
关键词：
primes; almost primes; sieve method; exponential sums; 11D61;
D O I：
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学科分类号：
摘要：
We show that for any integers a and m with m ≥ 1 and gcd(a,m) = 1, there is a solution to the congruence pr ≡ a (modm) where p is prime, r is a product of at most k = 17 prime factors and p, r ≤ m. This is a relaxed version of the still open question, studied by P. Erdős, A. M. Odlyzko and A. Sárközy, that corresponds to k = 1 (that is, to products of two primes).
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页码：55 / 61
页数：6
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