the equation is n^2-n+2
let n=1 then
1^2-1+2=2 which is divisible by 2 hence its true for n=1.
now let it be true for n=k therfor
now let us consider n=k+1
=2(r+k) which is divisible by 2
hence whenever it is true for k it is also true for k+1
hence by PMI n^2-n+2 is divisible by 2