5 problems

Let $k\geq 3$ and let $\vec{\mathbf{v}}\in\mathbb{Z}^{k-1}\setminus\{\vec{\mathbf{0}}\}$. In the Large Steps Algorithm, let $j_{\mathrm{lsb}}$ denote the bound on the largest index…

Let $N$ be a natural number for which there exist antipalindromic numbers $A$ and $B$ with $N=A/B$, and measure the size of a solution by the length of the relevant base-$2$ repres…

Let $N$ be a natural number for which there exist palindromic numbers $A$ and $B$ with $N=A/B$, and measure the size of a solution by the length of the relevant base-$2$ representa…

For a natural number $N$, consider the heuristic algorithm used to search for palindromic numbers $A$ and $B$ satisfying $N=A/B$. Nontermination conjecture. There are infinitely ma…

Let $\mathbf t=(t_0,\ldots,t_{d-2})$ and … where $N,b_0,\ldots,b_{d-2}$ are integers, $N\equiv\sum_{i=0}^{d-2}b_i^2\pmod q$, and $\gcd(N,q)=1$. For $r>0$, let … The sum-of-two-squa…