A note on primes p with $σ(p^m)=z^n$
نویسندگان
چکیده
منابع مشابه
A Note on Artinian Primes and Second Modules
Prime submodules and artinian prime modules are characterized. Furthermore, some previous results on prime modules and second modules are generalized.
متن کاملA note on primes in short intervals
This paper is concerned with the number of primes in short intervals. We present a method to use mean value estimates for the number of primes in (x, x+x] to obtain the asymptotic behavior of ψ(x+x)−ψ(x). The main idea is to use the properties of the exceptional set for the distribution of primes in short intervals. Mathematics Subject Classification (2000). 11NO5.
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For integers a and b we deene the Shanks chain p 1 ; p 2 ; : : : ; p k of length k to be a sequence of k primes such that p i+1 = ap i 2 ? b for i = 1; 2; : : : ; k ? 1. While for Cunningham chains it is conjectured that innnitely long chains exist, this is, in general, not true for Shanks chains. In fact, with s = ab we show that for all but 56 values of s 1000 any corresponding Shanks chain m...
متن کاملA note on Primes in Short Intervals
Instead of a strong quantitative form of the Hardy-Littlewood prime k-tuple conjecture, one can assume an average form of it and still obtains the same distribution result on ψ(x + h) − ψ(x) by Montgomery and Soundararajan [1].
متن کاملa note on finite groups with the indice of some maximal subgroups being primes
the theorem 12 in [a note on $p$-nilpotence and solvability of finite groups, j. algebra 321(2009) 1555--1560.] investigated the non-abelian simple groups in which some maximal subgroups have primes indice. in this note we show that this result can be applied to prove that the finite groups in which every non-nilpotent maximal subgroup has prime index aresolvable.
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1991
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-62-2-193-196