Question

Show that any positive integer is of the form 3q or 3q+1 or 3q+2

Answer 1

Answer:

let a be any positive integer with b=3.

we shall aplly euclids division lemma.

a=bq+r(0<=r<b)

possible values for r are o, 1,2

put r =0, we get

a=3q+0

a=3q.

put r=1, we get

a=3q+1

now put r=2 we get

a=3q+2

hence proved that any positive integer is of the form 3q or3q+1 or3q+2.