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Find the largest positive integer n such that
\frac{(n + 1)^2}{n + 2}
is an integer.

 Jul 25, 2024
 #1
avatar+129842 
+1

(n + 1)^2 = n^2 + 2n + 1

 

            n

n + 2  [ n^2 + 2n + 1 ] 

            n^2 + 2n

            ___________

                             1

 

Note that this will never produce an integer because we will always have a remainder of  1 / (n + 2)

 

cool cool cool

 Jul 25, 2024

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