Use mathematical induction to prove that the statement is true for every positive integer n.
2 is a factor of n2 - n + 2

Question

Use mathematical induction to prove that the statement is true for every positive integer n. 
2 is a factor of n2 - n + 2

anonymous · Answer

Do you know the steps for mathematical induction?

anonymous · Answer

Not an induction proof, though nothing is stopping you from doing so... Here's one way you can reason that $n^2-n+2$ must be even.

Any even number plus 2 will be even, so you can ignore that part. Factoring, you have
$$n^2-n=n(n-1)$$
which is the product of an integer and the integer preceding it. If $n$ is odd, then $n-1$ is even. The product of an odd and an even gives you an even. Add 2 and it's still even. The same applies in the case that $n$ is even and $n-1$ is odd.

anonymous · Answer

The question says use mathematical induction which requires 3 steps, I'm pretty sure here teacher will mark her off for not doing it in that way and giving that explanation you gave above, not going aginst you but I think that's her instructions

anonymous · Answer

I understand, I was just giving a general argument. You can reconstruct the argument I provided so that it can involve a proof by induction (the claim that $n(n-1)$ is always even, for example).