Consider the following theorem: There do not exist three consecutive odd integers a, b and c such that a² + b² = c². Example of three consecutive odd integers can be 1,3,5. a) Restate the theorem into a conditional statement or implication (p⇒q): If a,b and c are consecutive odd integers, then a^2 c^2. Put your answer in the blank as "is equal to" or "isn't equal to". +b^2 b) Fill in the blanks in the following proof of the theorem. Proof: Let a,b, and c be consecutive odd integers. Then a=2k+1, b= Suppose a² + b² = c². Then (2k + 1)²+1 and c=2k+5 for some integer k. )^2=(2k+5)². =0. Thus, k = or k= If follows that 8k² + 16k + 10 = 4k² + 20k + 25 and 4k² - 4k- This contradicts k being an Therefore, there does not exist three consecutive odd integers a,b and c such that a² + b² = c².

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