Example 3.3: (arithmetic progression basis) let x be the set of positive
integers and consider the collection b of all arithmetic progressions of posi-
tive integers. then b is a basis. if me x then b : = {m+(n-1)p} contains
m. next consider two arithmetic progressions b1: = {a1 + (n - 1)p1} and
b2 = {a2 + (n - 1)p2} containing an integer m. then b : = {m + (n -1) (p)}
does the job for p : = lcm{p1, p2}: