# Publications and Preprints

On lattice points where all nearby points are not relatively prime
by
Shanta Laishram and Florian Luca
Given positive integers $a, b$, let $M=M(a, b)$ and $N=N(a, b)$ be a minimal pair of positive integers such that we always have gcd$(M-i, N-j)>1$ for all $1\leq i\le a$ and $1\leq j\le b$. We give upper and lower bounds for $M, N$.

isid/ms/2015/16 [fulltext]