All Questions

If $P=\sum_{\bf i} a_{\bf i}x^{\bf i}\in {\mathbb Z}[x_1,\dots,x_d]$, let $|P|=\sum_{\bf i}|a_{\bf i}|x^{\bf i}$ and $h(P)=|P|(2,\dots,2)$, so that there is only a finite number of $P$ with $h(P)\leq ...

A multilinear polynomial $f\in\mathbb Z[x_1,\dots,x_t]$ has terms only of form $$b\prod_{i=1}^tx_i^{a_i}$$ where $a_i\in\{0,1\}$ and $b\in\mathbb Z$. Is there no general purpose algorithm for ...

Say that a Diophantine equation is almost-satisfiable iff for each $n\in\mathbb{N}$ it has a solution mod $n$. Trivially genuine satisfiability over $\mathbb{N}$ implies almost-satisfiability, but the ...

Given a Diophantine equation it is not decidable if it has integer solution. I. Is there a Diophantine set $\mathcal D_{unique}$ satisfying the properties every member in $\mathcal D_{unique}$ is a ...