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Unformatted text preview: , . . . , k , where k 1. We want to show that x k +1 + 1 /x k +1 is an integer. We have ( x k +1 + 1 /x k +1 ) = ( x k + 1 /x k )( x + 1 /x )( x k1 + 1 /x k1 ) Now, the right hand side is an integer since ( x k + 1 /x k ) , ( x k1 + 1 /x k1 ), and ( x + 1 /x ) are all integers, the rst two by inductive hypothesis, the later by the original problems hypothesis. Hence the left hand side is an integer. By induction, x n + 1 /x n is an integer for all n N . Date : February 21th, 2008. 1...
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This note was uploaded on 06/15/2009 for the course MATH 74 taught by Professor Courtney during the Spring '07 term at University of California, Berkeley.
 Spring '07
 COURTNEY
 Division, Integers

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