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Prove that for any positive integer n, there is a k e Z>o and ao, a1, . .. , ak E {0,1} such that k n = i=0 (1 y. There are several ways to prove this, but one of them uses the fact that given a positive integer n, either n = or n = 2m + 1 for some m E Z. You may use this fact without proof if you'd like.) 2m for some m E Z

Prove that for any positive integer n, there is a k e Z>o and ao, a1, . .. , ak E {0,1} such that k n = i=0 (1 y. There are several ways to prove this, but one of them uses the fact that given a positive integer n, either n = or n = 2m + 1 for some m E Z. You may use this fact without proof if you'd like.) 2m for some m E Z

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.2: Properties Of Group Elements
Problem 30E: 30. Prove statement of Theorem : for all integers .
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maybe by induction. not sure
Prove that for any positive integer n, there is a k e Z>o and ao, a1, . .. , ak E {0,1} such that k n = i=0 y. There are several ways to prove this, but one of them uses the fact that given a positive integer n, either n = or n = 2m + 1 for some m E Z. You may use this fact without proof if you'd like.) 2m for some m E Z
Transcribed Image Text:Prove that for any positive integer n, there is a k e Z>o and ao, a1, . .. , ak E {0,1} such that k n = i=0 y. There are several ways to prove this, but one of them uses the fact that given a positive integer n, either n = or n = 2m + 1 for some m E Z. You may use this fact without proof if you'd like.) 2m for some m E Z
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