Question 1207642
<pre>

I wish you wouldn't use notation incompatible with HTML.

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Find the largest positive integer n such that

{{{(n+1)^2/(n+2)}}} is an integer?

I don't think it ever can be a positive integer if n is a positive integer.
Let's see why:

{{{(n^2+2n+1)/(n+2^"")}}}

Divide it out by long division:

     <u>        n + 0</u>
n + 2) n<sup>2</sup> + 2n + 1
       <u>n<sup>2</sup> + 2n</u>
            0n + 1
            <u>0n + 0</u>
                 1   
       
{{{(n^2+2n+1)/(n+2)}}}{{{""=""}}}{{{n+1/(n+2)}}} and thus will never be a positive 
integer, because {{{1/(n+2)}}} will always be a fraction and will
never be a positive integer to add to positive integer n to 
give a positive integer.

Edwin</pre>