Geodesic
Rectangles of nonvisible lattice points
Journal of integer sequences, Tome 18 (2015) no. 10.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: A lattice point (0, 0) $\ne (x, y) \in Z^{2}$ is called $visible$ (from the origin) if $gcd(x, y)=1$, and $nonvisible$ otherwise. Given positive integers $a, b$, define $M := M(a, b)$ and $N := N(a, b)$ to be the positive integers $M$ and $N$ having the least value of $max(M, N)$ with the property that $gcd(M-i, N-j)$ > 1 for all $1 \le i \le a$ and $1 \le j \le b$. We give upper and lower bounds for $M, N$.
Classification : 11N37, 11P21, 11H06
Keywords: prime number, chinese remainder theorem, lattice point, visibility, greatest common divisor 
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     author = {Laishram, Shanta and Luca, Florian},
     title = {Rectangles of nonvisible lattice points},
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     year = {2015},
     language = {en},
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Laishram, Shanta; Luca, Florian. Rectangles of nonvisible lattice points. Journal of integer sequences, Tome 18 (2015) no. 10. http://geodesic.mathdoc.fr/item/JIS_2015__18_10_a6/