# How to prove that this statement is true for every positive integer n?(see picture. Thanks!

Feb 6, 2018

if n^2-n+2 is pair, (n+1)^2-(n+1)+2" is also pair

#### Explanation:

For n=1: ${n}^{2} - n + 2 = 2$

If $\textcolor{p u r p \le}{{n}^{2}} - \textcolor{red}{n} + 2$ is pair

then:

$\textcolor{p u r p \le}{\left({n}^{2} + 2 n + 1\right)} - \textcolor{red}{\left(n - 1\right)} + 2$

n^2−n+2 +2n+1 +1+2

color(blue)(n^2−n+2) +2n+4#,

,2n+4 is obviuously pai so the thesis is proved