Question 1205414
<pre>
Ikleyn is apparently not familiar with the standard 
notation of Z for the set of all integers.  I had
forgotten it myself and did not notice it. But the
solution by MathLover1 is the correct one. Mine at
the top is correct for the actual maximum value of
k but required some "eyeballing" to find the actual
maximum, assuming x and y to be integers.  Copied
from the internet:<i>

The set of integers is represented by the letter Z. 
An integer is any number in the infinite set,

Z = {..., -3, -2, -1, 0, 1, 2, 3, ...}

Integers are sometimes split into 3 subsets, 

{{{Z^"+"}}}, {{{Z^"-"}}} and {0}. {{{Z^"+"}}} is the 
set of all positive integers (1, 2, 3, ...), while {{{Z^"-"}}}
is the set of all negative integers (..., -3, -2, -1). 
Zero is not included in either of these sets . {{{Z^nonneg}}} 
is the set of all positive integers and 0, while {{{Z^nonpos}}} 
is the set of all negative integers and 0.</i> 

Edwin</pre>