Gerhard Paseman
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 Jan 12 awarded Yearling Jan 9 awarded Nice Question Nov 16 awarded Nice Answer Nov 3 awarded Nice Answer Nov 2 revised Proof that the factors of sigma(p^e) have two forms LateXed for readability. Hopefully someone can \center the forms of numeric factors of X. Nov 2 reviewed Approve The classical two phase Stefan problems Nov 2 comment What is known about the largest prime divisor of the product of $k$ consecutive integers? You might be interested in a paper of Filip Najman at arxiv.org/abs/1108.3710 . The largest prime divisor of the product n+1 to n +f(k) is looked at and shown to be larger than k when n is larger than k. f(k) is pretty small and conjectured to be O(log(k)^2). So you don't need as many as k consecutive integers. Gerhard "Sees This As Smooth Intervals" Paseman, 2015.11.02 Oct 30 comment Making integer multisets graphic Here is another idea which may get $k$ down to around $(b\log b)/m$. Start by picking $k = \lceil b/m \rceil$ and create a graphical fragment using $k$ columns. Hook up as many of these as you can to reduce the maximal number of unconnected edges at any vertex. Now double the fragment and hook up remaining edges between fragments. Iterate the doubling process until done. This may end up terminating quickly. Gerhard "Leaves The Analysis To You" Paseman, 2015.10.30. Oct 30 comment Making integer multisets graphic Another obvious observation is that $km \gt b$. This really hinges on the maximal degree. It may be worth expressing $k$ as a function of $b/m$. Gerhard "Happy All Hallows Eve Eve" Paseman, 2015.10.30 Oct 30 revised Making integer multisets graphic fix arithmetic and notation Oct 30 comment Recognize this countably generated abelian group? Uh, if $q=1$, the group is no longer infinitely generated. I think the condition $1 \lt q \lt p$ shows where the interesting part is. I do like that your answer does cover the case $q=1$. Gerhard "For My Idea Of Interesting" Paseman, 2015.10.30 Oct 30 revised Making integer multisets graphic added 12 characters in body Oct 30 revised Making integer multisets graphic edited body Oct 30 answered Making integer multisets graphic Oct 30 comment Making integer multisets graphic Is $X$ the set of degree values? If so, and if $b$ is the largest value of $X$, then in general $k \leq b$ (need $b+1$ when $M$ is a singleton). Gerhard "Will Add More With Confirmation" Paseman, 2015.10.30 Oct 29 reviewed Approve An identity for the cosine function Oct 23 revised Cyclotomic polynomials: $\Phi_n(p)$ is like $p^{\phi(n)}$ for big enough $p$, right? added 8 characters in body Oct 23 revised Cyclotomic polynomials: $\Phi_n(p)$ is like $p^{\phi(n)}$ for big enough $p$, right? more acknowledgment and refined answer Oct 23 comment Cyclotomic polynomials: $\Phi_n(p)$ is like $p^{\phi(n)}$ for big enough $p$, right? I did, and it got reverted to Jamseon Thanks for the catch. Gerhard "Still Have Seoul Inside Me" Paseman, 2015.10.23 Oct 23 revised Cyclotomic polynomials: $\Phi_n(p)$ is like $p^{\phi(n)}$ for big enough $p$, right? edited body