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 3n≥n3+1 forn≥4. (Hint. Note that 3·(n3+1)−(n+1)3−1 =n3+n(n−4)(n+ 1) +n+ 1≥0 whenn≥4.)Solution.