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title{Solutions to Velleman's "How to Prove It"}
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section{Introduction}
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Exercise 1 (a): Using the formula $2^{15}-1 = 2^{3 cdot 5}-1$ where $a = 5, b = 3$ then $2^b-1 = 2^3-1 = 7$ and $1+2^b+2^{ncdot b}+...+2^{(a-1)cdot b} =
1+2^3+2^{2cdot3}+2^{3cdot3}+2^{4cdot3} = 4681$

Exercise 1 (b): $2^{32767}-1 = 2{7cdot4681}-1$ where $b = 7$, so $x = 2^7-1 = 127$

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