Please use No17 And NO18 together to solve the problem.

c) Use structural induction to she is a positive integer. (a, b) e S defined recursively by Basis step (0,0) S A +2-----1+Jzx27. Let S be the subset of the set of or f2x-1-1 when n is a positive integer. 17. Determine the number of divisions used by the Euclidean algorithm to find the greatest common divisor of the Fi- bonscci numbers J and Jntl, where n is a nonnegative integer.Verify your answer using mathematical induction. Recursive step If (a, b) e S (a + L,b+ 1) c S, and (a +2,b n) List the elements of S produc plications of the recursive def b) Use strong induction on the nu the recursive step of the definiti 18. Let Show that whenever (a,b) e S e) Use structural induction to sh In Jn I when n is a positive integer Exercise I8. prove the idenlity given in lExercise 14. (Re call that the determinant of the matrix 28. Givearecursive delinition of cach pairs of positive integers. IHint l in the plane and look for lines c ) 19. By taking determinants of hoth sides of the equation in set.l