On the prime power factorization of n!

Mathematics – Number Theory

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

7 pages; accepted Journal of Number Theory

Scientific paper

In this paper we prove two results. The first theorem uses a paper of Kim \cite{K} to show that for fixed primes $p_1,...,p_k$, and for fixed integers $m_1,...,m_k$, with $p_i\not|m_i$, the numbers $(e_{p_1}(n),...,e_{p_k}(n))$ are uniformly distributed modulo $(m_1,...,m_k)$, where $e_p(n)$ is the order of the prime $p$ in the factorization of $n!$. That implies one of Sander's conjecture from \cite{S}, for any set of odd primes. Berend \cite{B} asks to find the fastest growing function $f(x)$ so that for large $x$ and any given finite sequence $\epsilon_i\in \{0,1\}, i\le f(x)$, there exists $n

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

On the prime power factorization of n! does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the prime power factorization of n!, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the prime power factorization of n! will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-349568

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.