Find the mistakes in the “proofs” shown.
Exercise
Theorem: For all integers k, if k > 0 then k2 + 2k + 1 is composite.
“Proof: For k = 2, k2 + 2k + 1 = 22 + 2 • 2 + 1 = 9. But 9 = 3 • 3, and so 9 is composite. Hence the theorem is true.”
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