All Questions

For integers $n\ge k\ge0$, let $p(n,k)$ denote the number of ways to write $n$ as a sum of $k$ positive integers (repetition allowed). For example, $p(6,3)=3$ since $$6=1+1+4=1+2+3=2+2+2.$$ QUESTION. ...

rowlands sequence is defined as follows \begin{equation} a_{n}=a_{n-1} + b_{n} \end{equation} where $b_{n} = gcd(a_{n-1}, n)$ for $n>h$ it originates from E. Rowlands 2008 paper "A Natural ...

Let $n$ be any integer greater than $2^{10^6}$. Given any $s\le (\log_2 n)/1000$ integers $1=q_1\le q_2\le \cdots q_{s-1}\le q_s=n$. Prove that $$\min_\ell\left(\sum_{i=1}^\ell q_i\right)\left(\sum_{i=...

I have worked on a Diophantine equation by using transcendental and reduction methods given by Baker and Davenport. However, to solve completely the equation I have one complicated case and I proved ...