exercises on recursive definition of set

Q1. give a recursive definition for the set of ordered pair of positive intergers, S={(a, b)| a, b are positive intergers, and a|b}

 

Answer:

basis step: (1, 1) belongs to S;

recursive step: if (a, b) belongs to S, (a, a+b) belongs to S, and (a+1, a+1) belongs to S.