Question 1106017
-----------------------------------------------------
A positive integer number increased by its square
----------------------------------------------------

{{{n+n^2}}}



--------------------------------------------------------------
 is equal to 81 times the next higher positive integer number.
---------------------------------------------------------------


{{{previousdescription=81(n+1)}}}




-------------------------
Find the number.
-------------------------

{{{highlight_green(n+n^2=81(n+1))}}}


-

factorize left side,
{{{n(1+n)=81(n+1)}}}
{{{n(n+1)=81(n+1)}}}
-
{{{highlight(n=81)}}}