All Questions

Fix $n\in\mathbb N$ and a starting polynomial (or seed) $p_n=a_0+a_1x+\dots+a_nx^n$ with $a_k\in\mathbb Z\ \forall k$ and $a_0a_n\ne0$. Define $p_{n+1},p_{n+2},\dots$ recursively by $p_r = p_{r-1}+...

I am writing a paper to accompany a Short Communication I plan to give in Rio this August. The paper regards work on jumping primes, a project on which Jose Brox has been working with me. I was going ...

Let $a(n)$ be A005225 i.e. number of permutations of length $n$ with equal cycles. Here $$ a(n)=n!\sum\limits_{d|n}\frac{1}{d!(\frac{n}{d})^d} $$ Let $$ R(n,q,z)=(q+1)R(n-1,q+1,z)+\sum\limits_{j=0}^{q}...

Given $n$, what is the largest set of consecutive integers in $[n,2n]$ can we have so that each integer is divisible by a distinct element from $[\log n,2\log n]$ (no partiular order)? So apriori I am ...