<PRE><B>Question 1137879</B>
Ans {{{ highlight( 2022 ) }}}

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Workout:
(Assumes a and b are any integers):&lt;br&gt;
  
For {{{ a&gt;=0 }}}:&lt;br&gt;

   a/(a+6) &lt; 2017/2023
     2023a  &lt; 2017(a+6)
     2023a  &lt; 2017a + 12102
        6a  &lt; 12102
         a  &lt; 2017&lt;br&gt;

So that gives the 2017 fractions  0/6, 1/7, ..., 2016/2022&lt;br&gt;

Now for {{{ a&lt;0 }}} :
     -1/5, -2/4, -3/3, -4/2 and -5/1  are all &lt; 2017/2023
This is an additional 5 fractions. &lt;br&gt;

Continuing with negative integers:
 -6/0  is undefined
 -7/-1  is  7  &gt; 2017/2023&lt;br&gt;

For all other negative integers a/(a+6) &gt; 1 &gt; 2017/2023  (the magnitude of (a) is greater than (a+6) for all these numbers) &lt;br&gt;

  2017 + 5 = 2022



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