Theoretical Statistics and Mathematics Unit, ISI Delhi

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]

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