The Lonely Runner Conjecture, posed independently by Wills and by Cusick, states that for any set of runners running along the unit circle with constant different speeds and starting at the same point, there is a time where ...

For the well known Frobenius problem, we present a new geometric approach, based on the use of the $n$-dimensional lattice $\mathbb{Z}^n$, where $n$ is the number of generators. Within this approach we are able to study ...