Question 438234
{{{n^2 - n + 2}}}
Let n be any even integer.  ==> n = 2k ==>{{{n^2 - n + 2 = 4k^2 - 2k + 2 = 

2(2k^2 - k + 1)}}}, hence the expression is even.

Let n be odd.  ==> n = 2k-1 ==> {{{n^2 - n + 2 = 4k^2 - 4k + 1 - 2k + 1 + 2

= 4k^2-6k + 4 = 2(2k^2 - 3k + 2)}}}, and so again the expression is even.