structural induction

Hey everyone,

So I am having a problem with this question:


Let S be the subset of a set of ordered pairs of integers defined recursivley by

Basic step: (0,0) is an element of S
recursive step: if (a,b) is an element of S, then (a+2, b+3) is an element of S and (a+3, b+2) is an element of S.

1. use strong induction on the number of applications of the recursive test of the definition to show that 5|a+b when (a,b) is an element of of S.

2. usestructural induction to show that 5| a + b when (a,b) is an element of S.


Can anyone explain how to do this.

Thanks in advance,

Discreteman