1. (Divisibility) Let a, b e Z with a # 0. We say that a divides b if there is some integer k such that b a k. For example, 3 divides 15 since 15 3 5 and 5 € Z. Use mathematical induction to show that if a and b are distinct integers then a b divides a"- b for every positive integer n. %3D

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Provide NEAT and COMPLETE solutions to the following problems.

1. (Divisibility) Let a, b e Z with a 0. We say that a divides b if there is some integer k
such that b = a k. For example, 3 divides 15 since 15 3 5 and 5 E Z. Use mathematical
induction to show that if a and b are distinct integers then a b divides a"-b" for every
positive integer n.
Transcribed Image Text:1. (Divisibility) Let a, b e Z with a 0. We say that a divides b if there is some integer k such that b = a k. For example, 3 divides 15 since 15 3 5 and 5 E Z. Use mathematical induction to show that if a and b are distinct integers then a b divides a"-b" for every positive integer n.
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