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Unformatted text preview: c : d . a 1 ;:::; a n / as well as integers s 1 ;s 2 ;:::;s n such g : c : d .a 1 ;:::;a n / D s 1 a 1 C s 2 a 2 C C s n a n : Exercises 1.6 1.6.1. Complete the following sketch of a proof of Proposition 1.6.7 using the wellordering principle. (a) If a , consider the set S of nonnegative integers that can be written in the form a sd , where s is an integer. Show that S is nonempty. (b) By the wellordering principle, S has a least element, which we write as r D a qd . Then we have a D qd C r . Show that that r < d ....
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 Fall '08
 EVERAGE
 Algebra, Integers

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