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Unformatted text preview: n; n + 10). 6. If m is an integer, then m Z = f mx : x 2 Z g is the set of all integer multiples of m . (a) If m and n are given integers, then give a precise description of the intersection m Z \ n Z : More precisely, m Z \ n Z = r Z for some integer r . Describe r in terms of m and n . (b) Similar to part (a), describe the set m Z + n Z = f mx + ny : x; y 2 Z g = s Z ; by describing the integer s . 7. Give a proof by induction to show that 5 2 n ¡ 1 is divisible by 24, for all positive integers n . Math 4023 1...
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This document was uploaded on 12/28/2011.
 Fall '09

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