All Questions

Suppose I have integers $a_1, \dots, a_n$ which are coprime, meaning that $$a_1 b_1 + \dots + a_n b_n = 1$$ has a solution in integers $b_1, \dots, b_n$. I would like to get a bound saying ...

Crossposted at Theoretical Computer Science SE A problem I study reduces to a system of linear equations $A\mathbf{x}=\mathbf{1}$ where $A$ is an $m\times n$ matrix with each entry $a_{ij}\in\{0,1\}$....

I have the following problem: $A x = b$ where $A, b$ - $m \times n$-matrix and $m$-vector of nonnegative integers (respectively). $x \in \{0,1\}^n $ - vector of binary variables, which need to be ...

Assume each entry is in $\Bbb Z$. Say we want to solve $Ax=b$ where known $A$ is $n\times n$, unknown $x$ is $n\times1$ and $b$ is $n\times1$. The absolute value of minors of augmented matrix $[A|b]$...

Let $n$ be positive integer, $k$,$B$ fixed positive integers. Let $f_i(x_1,x_2...x_n)$ be a system of $n-k$ linearly independent linear equations over the integers. Let $S(f_i,k,B)$ be the set of ...