5.71. Below is given a proof of a result. What result is proved? Proof Let a, b, Ce Z such that a² + b² = c². Assume, to the contrary, that a, b and c are all odd. By (the contrapositive of) Theorem 3.12 O, a? and b? are both odd. Therefore, a? = 2r +1 and b = 2s +1 for integers r and s. Thus, a? + b² = 2r + 2s + 2 = 2 (r + s+1). Since r + s+1 is an integer, a? + b is even. However, a? + b² = c² and c2 is odd. This is a contradiction.

5.71. Below is given a proof of a result. What result is proved? Proof Let a, b, Ce Z such that a² + b² = c². Assume, to the contrary, that a, b and c are all odd. By (the contrapositive of) Theorem 3.12 O, a? and b? are both odd. Therefore, a? = 2r +1 and b = 2s +1 for integers r and s. Thus, a? + b² = 2r + 2s + 2 = 2 (r + s+1). Since r + s+1 is an integer, a? + b is even. However, a? + b² = c² and c2 is odd. This is a contradiction.

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Description: what mistakes are found in this proof 5.71. Below is given a proof of a result. What result is proved?Proof Let a, b, Ce Z such that a² + b² = c². Assume, to the contrary, that a, b and c are all odd. By (the contrapositive of) Theorem 3.12 O, a?and

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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