Question

show that any positive even integer is of the form 6k, 6k + 2 or 6k+ 4 where k is some integer​

Answer 1

Let a be any positive Even integer and b=6 by division Lemma There k is integer

a=6k+r. where 0<r<6

Then r=0,1,2,3,4,5

a=6k, a=6k+1, a=6k+2, a=6k+3,

a=6k+4, a=6k+5

a=6k ,a=6k+2, a=6k+4 {even integer}

Hence any positive even integer are form 6k, 6k+2, 6k+4