Show that any positive integer is of the form 3q, 3q+1, 3q+2, where q is some integer

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

1.	Show that any positive integer is of the form 3q, 3q+1, 3q+2, where q is some integer
Answer» Let p be any positive integer and b = 3. Applying division Lemma with p and b =3 ,we havep = 3q + r, where 0 {tex}\\leq{/tex}\xa0r < 3 and q is some integerSo r=0,1,2If r=0 , p=3qIf r=1, p=3q+1If r=2, p=3q+2Therefore any positive integer is of form 3q,3q+1,3q+2 for some integer q.