Exam (elaborations)
How To Prove It: A Structured Approach Third Edition Solutions Manual
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1. We use the formula 2ab − 1 = (2b − 1)(1 + 2b + 22b + + 2(a−1)b) from the proof of Conjecture 2. (a) 215 − 1 = 23•5 − 1 = (25 − 1) • (1 + 25 + 210) = 31 • 1057. (b) 232,767−1 = 21057•31−1 = (231−1)(1+231+• • •+21056•31). The first factor is 231−1 = 2,147,48...
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