2
votes
2answers
582 views

Finding a basis for the solution space of a system of Diophantine equations

Let $m$, $n$, and $q$ be positive integers, with $m \ge n$. Let $\mathbf{A} \in \mathbb{Z}^{n \times m}_q$ be a matrix. Consider the following set: $S = \big\{ \mathbf{y} \in \mathbb{Z}^m \mid ...
5
votes
1answer
2k views

Integer solutions (lattice points) to arbitrary circles

Wolfram Alpha will provide integer solutions to arbitrary circle equations. I'm trying to understand how it's able to calculate them, but despite a fair bit of digging I haven't found any discussion ...