Journal of Integer Sequences, Vol. 18 (2015), Article 15.10.8 |

Stat-Math Unit

Indian Statistical Institute

7 S. J. S. Sansanwal Marg

New Delhi, 110016 India

Florian Luca

School of Mathematics

University of the Witwatersrand

P. O. Box X3

Wits 2050

South Africa

**Abstract:**

A lattice point (0, 0) ≠
(*x*, *y*) ∈ **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 ≤ *i* ≤ *a* and 1 ≤ *j* ≤ *b*.
We give upper and lower bounds
for *M*, *N*.

(Concerned with sequence A052157.)

Received May 7 2015;
revised versions received October 12 2015; October 24 2015;
October 27 2015.
Published in *Journal of Integer Sequences*, October 29 2015.

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