Find the main errors in the following “Proofs” and write down your own correct proofs. Let k be an integer. If k > 0, then k
2 + 2k + 1 is composite.
“Proof:” For k = 2, k
2 + 2k + 1 = 22 + 2 · 2 + 1 = 9. But 9 = 3 · 3, and so 9 is
composite. Hence, the theorem is true.