Geodesic
Rectangles of nonvisible lattice points
Journal of integer sequences, Tome 18 (2015) no. 10
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 
@article{JIS_2015__18_10_a6,
     author = {Laishram,  Shanta and Luca,  Florian},
     title = {Rectangles of nonvisible lattice points},
     journal = {Journal of integer sequences},
     year = {2015},
     volume = {18},
     number = {10},
     zbl = {1390.11117},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2015__18_10_a6/}
}
TY  - JOUR
AU  - Laishram,  Shanta
AU  - Luca,  Florian
TI  - Rectangles of nonvisible lattice points
JO  - Journal of integer sequences
PY  - 2015
VL  - 18
IS  - 10
UR  - http://geodesic.mathdoc.fr/item/JIS_2015__18_10_a6/
LA  - en
ID  - JIS_2015__18_10_a6
ER  - 
%0 Journal Article
%A Laishram,  Shanta
%A Luca,  Florian
%T Rectangles of nonvisible lattice points
%J Journal of integer sequences
%D 2015
%V 18
%N 10
%U http://geodesic.mathdoc.fr/item/JIS_2015__18_10_a6/
%G en
%F JIS_2015__18_10_a6
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/