Let S be the subset of the set of ordered pairs of integers defined recursively by:
(0, 0) element of S If (a, b) element of S, then (a+2, b+3) element of S and (a+3, b+2) element of S.
a) List the elements of S produced by the first 5 applications of the recursive definition.
b) Use mathematical induction or strong induction to show that 5 | a + b when (a, b) element of S.
c) Use structural induction to show that 5 | a + b when (a, b) element of S.