Adjacent Relative-Prime #s In Grid

[Olivier Gerard]

Dear Leroy,

in your search did you find squares with a toric 
completion (opposite ends are also relatively
prime, this is not the case in your example as (3,15) or
(21,15) are a problem), and squares with diagonal
relative primality also ?

Have you tried hexagonal and other figured numbers patterns ?

Olivier


Le 02, Leroy Quet écrivait:
> For an n-by-n grid, how many ways are there to place the integers 1
> through n^2 in the grid, one integer per grid-square, such that each
> integer is relatively prime to the integers adjacent to it
> (above/below/right/left)?
> 
> An n=5 example:
> 
> 15  2   5   4   3
> 
> 22  17  18  19  8
> 
> 7   6   25  24  11
> 
> 20  13  12  23  10
> 
> 21  16  1   14  9 
> 
> 
> Thanks,
> Leroy Quet