Rectangles Of Nonvisible Lattice Points
Shanta Laishram
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) ∈ Z2
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.
Full version: pdf,
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(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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