Homework 1 Solutions on Elementary Number Theory - MAS...

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MAS 4214/001 Elementary Number Theory, Fall 2014CRN: 80544Answers, Set 1Question 1. (2 pts) The aim of this problem is to compare the values of 3nandn3+ 1 for different values ofn.(a) By constructing a table, compare the values of 3nandn3+ 1 forn= 0,1,2,3,4,5.(b) Use mathematical induction to show that 3nn3+1 forn4. (Hint. Note that 3·(n3+1)(n+1)31 =n3+n(n4)(n+ 1) +n+ 10 whenn4.)Solution.

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