(a) Let k be in the set ofN.Prove that if k^2+k+5 is even, then (k+1)^2 +(k+1) +5 is even.

Well, since I wasn't sure how to prove this by induction, I did it by contrapositive and it worked out. Is that the correct way to do it?

(b) What is the value of k^2+k+5 when k = 7... Fairly straightforward, I got 61.

(c) What information do (a) and (b) provide?

Part a and c are where I am confused.

If I did part a correctly, then k^2+k+5 was proven to be even, but part b has proved otherwise.. What gives?